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# a basic algebra "problem" 10 frih\$

Manuel
-5^2= ???

what is the above equal to?
GSIS
IIRC that would be -5 x -5 which is equal to +25.

Excel agrees.
Manuel
Just what I thought...

That´s incorrect.

Keep trying
ocalhoun
What do you mean its incorrect?
-5^2=25 Simple; just whip out the calculator and try it!
If your problem is that the square root of 25 is not -5, that is baseless. In reality, the square root of 25 is positive or negative 5, either of which can be squared to get 25 (though the -5 possibility is often ignored).
Manuel
 ocalhoun wrote: What do you mean its incorrect? -5^2=25 Simple; just whip out the calculator and try it! If your problem is that the square root of 25 is not -5, that is baseless. In reality, the square root of 25 is positive or negative 5, either of which can be squared to get 25 (though the -5 possibility is often ignored).

I know that the square root may be positive or negative, and I am not basing the correct answer on a root.

With some basic algebra knowledge you would know that it is incorrect.
GSIS
 Manuel wrote: Just what I thought... That´s incorrect. Keep trying

Wouldn't waste my time.

Explain why it's incorrect.
Manuel
I´ll explain you for 10 frih\$.

If u accept, I wont reveal the explanation here because other members may participate.

That´s what I can do for you. If you do not want to, you will have to wait till a lot of members participate and someone gives the right answer, if no one does, I will give it, but a lot of time may have passed already
imagefree

-5^2 = -5*5=-25
Manuel
 imagefree wrote: the answer is -25. -5^2 = -5*5=-25

Finally!

Congratulations!!!

-5^2= -(5*5)= -25

(-5)^2= (-5 * -5)= 25

ocalhoun
 imagefree wrote: -5^2 = -5*5=-25

-5^2=-5*-5
-5^2 does not equal -5*5!
Doubt it?
What is -5^3?
imagefree
ocalhoun wrote:
 imagefree wrote: -5^2 = -5*5=-25

-5^2=-5*-5
-5^2 does not equal -5*5!
Doubt it?
What is -5^3?

^ means the power of the forst number and the number after ^ is the power.

5^2 means 5 raised to power 2=5*5=25

Got it?
ocalhoun
 imagefree wrote: 5^2 means 5 raised to power 2=5*5=25

That is correct.
but, -5^2 still does not equal -5*5!

You still haven't answered my question: according to your error-prone mathematics, what is -5^3 (expressed as _*_*_)?

Instructions that should be educational for you:
1: Click the windows start menu.
2: Click run...
3: In the run dialog, type in "calc", then <enter>
4: In the calculator window, click 'View'
5: Click 'Scientific' in the view menu
6: Click the '5' button.
7: Click the '+/-' button to make it negative.
8: Click the 'x^2' button to square it
9: Note the result.

For x^2<0
There is no real number that x could be.
imagefree
ocalhoun wrote:
 imagefree wrote: 5^2 means 5 raised to power 2=5*5=25

That is correct.
but, -5^2 still does not equal -5*5!

You still haven't answered my question: according to your error-prone mathematics, what is -5^3 (expressed as _*_*_)?

Instructions that should be educational for you:
1: Click the windows start menu.
2: Click run...
3: In the run dialog, type in "calc", then <enter>
4: In the calculator window, click 'View'
5: Click 'Scientific' in the view menu
6: Click the '5' button.
7: Click the '+/-' button to make it negative.
8: Click the 'x^2' button to square it
9: Note the result.

For x^2<0
There is no real number that x could be.

Ohhh I seeee!!!!!!!!

There seems to be a very basic problem.
Ok!! I am trying to solve it.

So friend Go and Open Calculator (may be using run box).
Type 5 then - and then X^2 to squair it.

What will happen? The "X^2" button takes the squair of the whole number. And remember!!!!!!!! it takes "-5" as X. So, taking the squair of -5 is obviously 25 Possitive.

On the other hand, the problem given in this contest is tricky. The actual math is not like how the Calculator work, and how the Programing languages work. (Also at some points calculator and languages like c become more strict). In actual math the expression is

-5^2=-25 (even on my personal Scientific Calculator)
While on windows' calculator, it will result 25. Its the difference.

There is a lot of stuff to tell you about this. If you still not understand, i will post here.
Hammy
The true answer is 25... no matter wat you say. It's just one on them things that a calculator doesnt understand and you have to understand it urself.

If u wrote -25 in an exam.. you would get it wrong.
Manus et Therion
-5 + -5 = -10 + -5 = -15 + -5 = -20 + -5 = -25

Is that not the long way around?
GSIS
 Manus et Therion wrote: -5 + -5 = -10 + -5 = -15 + -5 = -20 + -5 = -25 Is that not the long way around?

That would be 5 * (-5)

NOT

(-5) * (-5)
imagefree
GSIS wrote:
 Manus et Therion wrote: -5 + -5 = -10 + -5 = -15 + -5 = -20 + -5 = -25 Is that not the long way around?

That would be 5 * (-5)

NOT

(-5) * (-5)

Absolutely right. I agree.
Manuel
ocalhoun wrote:
 imagefree wrote: 5^2 means 5 raised to power 2=5*5=25

-5^2= -(5*5)= -25

THE "()" ARE VERY IMPORTANT.

If you do not beleive me then check kout the following book, so you can see I am right:

Intermediate Algebra by Jerome E. Kaufnamm & Karen schwitters(From Seminole Community College).

With the help of:

Cindy Fleck
Wright State University

Kay Haralson
Austin Peay State University

Kathryn T. McClellan
Tarrant Country Junior College-NorthEast

Sandra Mayo
Los Angeles Mission College

Reed Parr
Salt Lake Community College

C. L. Pinchback
University of Central Arkansas

Florida Community College at Jacksonvile

Mary Voxman
University of Idaho

Dennis W. Watson
Clark College

You guys a quite ignorant

You should study more
Hammy
why did u even post it?

If you got a question in a maths exam saying:

Simply the following:

a) -5^2
b) -5^3
c) -5^4

Wat wld u put?

If you just simply them.
a) -5 x -5
b) -5 x -5 x -5
c) -5 x -5 x -5 x -5

-5^2 <--- the 5 is a negative number.
Therefore.. -5 x -5 = 25.

-5^3 <--- the 5 is still a negative number.
Therefore... -5 x -5 x -5 = -125

-5^4 = -5 x -5 x -5 x -5 = .. err.. er... 625?

If you wanted the answer -25, the question would have to include the backets. -(5^2)

BODMAS
Brackets -- Orders -- Divide -- Multiply -- Addition -- Subtraction.

S - Subtraction does not include a minus (-) symbolizing a negative number.
and there you take the number as a whole negative number. which is where we get (-5 x -5).

100-5^2 ... This is where S in BODMAS work because it is a subtraction. the 5^2 is on it's own.
100--5^2 ... This as you know, the 5 is negative. It has to be.

Get me yet? I appologise for being ignorant.. but you even said..
 Quote: THE "()" ARE VERY IMPORTANT.

and indeed they are, Without them the answer = 25 ..
with them, the answer = -25.

Hammy.
Manuel
Haha

You keep duscusing on this.

You should not discuss if you do not have enough algebra knowledge.

Already told you to study and to check a good algebra book.
Hammy
You have no argument because im right...
And thanks, but i did pass my A-level maths.
imagefree
 Hammy wrote: -5^2 <--- the 5 is a negative number. Therefore.. -5 x -5 = 25.

Who told you 5 is a negative number in the above equation? 5 is a possitive number even without the ().
Friend!!! the main problem in this Question is the existance of Squair and the number is not covered by bracket. (Remember -5 is not like 0-5) now you may start arguing that -5=0-5 but the fact is what i told.

-5 in not equal to 0-5.
The red and blue - signs are different. Even the nature and application of both are different.

But the results are the same:
-5^2=-25
0-5^2=-25

SO, whats the difference? Can you tell @ Hammy? If you cant, i will.

The expression -5^2 necessarily means that there is existance of () around 5^2 and the equation below is true.

-5^2=-(5^2)

 Quote: You have no argument because im right... And thanks, but i did pass my A-level maths.

But the mathematics doesnt end at A Level.
Also just the studies without implementation are nothing.
If you learn any language like PHP, C, C++ etc, you better learn this point.
imagefree
ocalhoun wrote:
 imagefree wrote: -5^2 = -5*5=-25

-5^2=-5*-5
-5^2 does not equal -5*5!
Doubt it?
What is -5^3?

-5^3 results in -5*5*5 and the answer is -125 (although the answer you are thinking of is also 125, but the application of this negative sign is different.)
Hammy
You know that any number squared.. Negative or positive.. results in a postive number. So why are you fighting this?. :/

EDIT:
 Quote: But the results are the same: -5^2=-25 0-5^2=-25 SO, whats the difference? Can you tell @ Hammy? If you cant, i will.

Yes.. 1) is (MINUS 5) to the POWER of 2.
and.. 2) is 0 MINUS the (5 to the POWER of 2).
rohan2kool
ok.. we may have language restrictions, but Manuel, you are seriously and an idiot.

the function f(x) = x^2, is defined for all real values i.e it's domain is R. However, it's range is R - (-∞, 0) i.e, the output of the function is always a positive real value. I don't know if the knowledgeable algebra guy learnt functions wherever he studied math, but there is no real value in this world, no damn real value at all whose square would return a negative number. Complex solutions such that x < 0 exist, but -5 is a real number, not a complex number.

the only valid argument i found [from imagefree] was that the expression -x^2 evaluates to -(x^2) instead of (-x)^2. Only and only in that case -5^2 would evaluate to -25. That is true, because in standard argument, the exponential operator has precedence over the negation operator [Refer {2}]. Next the statement, 'that is not the way programming languages work'. Now, whoever was that idiot.. the '^' operator is an XOR operator in most of the languages. Try doing this in a language.. you'll get a different answer in different computers, because different processors use different sign notation. [Refer {1}]. And in no way would it be the square of 5, it would be the XOR of -5 and 2 (or the negative of XOR of 5 and 2, which will be same across almost all computers). Most of the languages don't even have an exponential operator as a standard operator. They rather have functions which use multiplication for exponentials. Even if it does have an operator, what the expression evaluates to has different implications in different programming languages depending on the operator precedence [Refere {2}].

Refer:

1: http://en.wikipedia.org/wiki/Signed_number_representations
2: http://en.wikipedia.org/wiki/Order_of_operations
imagefree
i have found a reference in favour of my solution

See!! it is copied from WIKIPEDIA.
imagefree
 GSIS wrote: IIRC that would be -5 x -5 which is equal to +25. Excel agrees.

Excel gives higher priority to negation than to exponentiation, which results in -5^2 = (-5)^2 = 25.
imagefree
Hammy wrote:
You know that any number squared.. Negative or positive.. results in a postive number. So why are you fighting this?. :/

EDIT:
 Quote: But the results are the same: -5^2=-25 0-5^2=-25 SO, whats the difference? Can you tell @ Hammy? If you cant, i will.

Yes.. 1) is (MINUS 5) to the POWER of 2.
and.. 2) is 0 MINUS the (5 to the POWER of 2).

Its not (Minus 5 ) to the Power of 2.
Its Minus (5 Power 2). Mathematics give priority to the exponent than the Unary operator -.
rohan2kool
did u seriously need to make 3 consecutive posts to make that point??
sonam
I am learning long time ago how the power have higher priority then minus (exclude here excel). In that case -5^2 is not same to -(5)^2. It is (-5)^2 and result is 25.

Sonam
Urban
Look, I'm 15 and I just got summer class in math (THE LAST WEEK!) because my class is full of tards (including me) and I got 87%. Minimum 5 questions in the exam was like this one and I got the good answer.

-5^2

=

-5²

=

-5*5

=

-25

Why? Because only the FIRST number is negative (in this case).

Now with:

(-5)^2

=

(-5)²

=

(-5)*(-5)

=

25
Arnie
Sonam is right... ^ is a higher priority than - (which is basically *, being *-1) so you first run 5^2=25 and only then the minus: -25. Brackets overrule ^ so (-5)^2 is 25.

The third power is more interesting. Like with all odd powers, -5^3 and (-5)^3 are the same, because (-5)^3 is also negative!
Manuel
 Urban wrote: Look, I'm 15 and I just got summer class in math (THE LAST WEEK!) because my class is full of tards (including me) and I got 87%. Minimum 5 questions in the exam was like this one and I got the good answer. -5^2 = -5² = -5*5 = -25 Why? Because only the FIRST number is negative (in this case). Now with: (-5)^2 = (-5)² = (-5)*(-5) = 25

Finally, someone that understands!!!

Congrats man, really!
imagefree
 Arnie wrote: Sonam is right... ^ is a higher priority than - (which is basically *, being *-1) so you first run 5^2=25 and only then the minus: -25. Brackets overrule ^ so (-5)^2 is 25. The third power is more interesting. Like with all odd powers, -5^3 and (-5)^3 are the same, because (-5)^3 is also negative!

If ^ has priority then ^ should be applied first, why are you applying negative sign to 5 before the squair??? Putting () around 5 and taking - sign inside means that - sign is applied first.

Arnie
 Quote: why are you applying negative sign to 5 before the squair???
I first ran 5^2, didn't I?
 Arnie wrote: so you first run 5^2=25 and only then the minus: -25

And after that I mentioned the different expression (-5)^2 to show that it's something different because of the brackets. I was not saying that -5^2 = (-5)^2 !!

But, after checking sonam's post I saw that what he did was wrong.
 Sonam wrote: In that case -5^2 is not same to -(5)^2. It is (-5)^2 and result is 25.
He was right about ^ being the higher priority, as I said in my previous post... but he just didn't apply it correctly (which I apparently didn't check.)

Let's do something more interesting now.
GSIS
My only hope, here, is that imagefree never works on a mission-critical system that depends on the squaring of a negative number ...
sonam
 Quote: He was right about ^ being the higher priority, as I said in my previous post... but he just didn't apply it correctly (which I apparently didn't check.

He, he, I know rules but I don't know mathematic.

Sonam
ocalhoun
 imagefree wrote: -5 in not equal to 0-5. If you learn any language like PHP, C, C++ etc, you better learn this point.

-5=0-5
How the heck can you dispute that?

What do programming languages have to do with this?

What's all this talk about the priority of the negative sign?
It's not an operation, just a part of the number: -5.
X^2=X*X
X=-5
imagefree
ocalhoun wrote:
 imagefree wrote: -5 in not equal to 0-5. If you learn any language like PHP, C, C++ etc, you better learn this point.

-5=0-5
How the heck can you dispute that?

What do programming languages have to do with this?

What's all this talk about the priority of the negative sign?
It's not an operation, just a part of the number: -5.
X^2=X*X
X=-5

You are still at the first point. I think you have to reread all the posts. The matter is resolved now.

By the way!!! X != -5. Its X=5.

Programming languages are the practical implementation of your mathematical skills.

Yes 0-5 = -5 but in fact -5 is not same as 0-5 and both are different. 0-5 results in -5, its true but the actual fact behind it is -5 has a negative sign that has different nature from other negative sign, and it applies to just one number or variable and it has priority over the negative sign that applies to 2 numbers. Take the following Example:

-3-4= ? obviously -7 because the priority goes to the Unary Operator - . Both - signs dont have equal hirarchy, and if you try to take them as equal, you will get 2 different answers.

This was what i tried to say.
imagefree
GSIS wrote:
 Manus et Therion wrote: -5 + -5 = -10 + -5 = -15 + -5 = -20 + -5 = -25 Is that not the long way around?

That would be 5 * (-5)

NOT

(-5) * (-5)

Really this solution best describes the problem.

-5 + -5 + -5 + -5 + -5 = -25
and it is the simplified form of the actual Question of this contest.
-5 + -5 = -10 + -5 = -15 + -5 = -20 + -5 = -25
-5 ( 1+1+1+1+1)=-25
-5(5)=-25
-(5^2)=-25
-5^2=-25

Here is the Hirerchy Table
Priority Up to down.
()
Squair and SQRT and other powers
Unary Operators
Multiply/ Divide
Plus/Minus
Arnie
There's no x in the question of the start post ocalhoun. Of course x² will be 25 when x=-5, because in x² the - only applies to x and the entire x is squared. Compare that to (-5)².

But in -5² the number you're primarily working with only seems to be -5, in fact it's 5 which you square and later make negative. Because the - applies to the entire expression 5². Compare that to -x² with x=5.

0-5 and -5 are different expressions with the same value. That's what -5=0-5 means. Strictly speaking the minus in -5 is a unary operation and the - in 0-5 is a binary operation. On some scientific calculators, they are different keys: the unary is a small - and the binary is bigger.
GSIS
The basic problem, here, is a lack of understanding.

We are talking about the difference between a negative number (-5), and a mathematical expression (0-5) which does not exist in the original question.

Had this expression existed the question would then have been:

x = 0-5^2

What is x?

If you enter the formula =0-5^2 into Excel the response is, indeed, -25. This is because Excel applies normal operator precedence.

However, =-5^2 returns +25. This is because the '-' indicates that the number to be squared IS negative - not that it is to be subtracted from 0.

Given the choice I think I'd accept Excel as correct rather than imagefree.

Perhaps imagefree would like to report this as a bug in Excel?
Arnie
Try asking a math teacher. He'll show you. I don't blame you for not having trust in random guys on forums, really, but -5² as it is written really is -25. Only (-5)² is 25.
GSIS
I'd prefer to accept what I was taught - by a maths teacher, oddly enough.

The square of any -ve number is, indeed, positive.

(-5) * (-5) = +25

The CUBE of a negative number would, of course, be negative:

(-5) * (-5) * (-5) = (+25) * (-5) = -125

The basic problem, in this thread, is simply one of understanding mathematical notation. Of understanding the difference in meaning of:

-5

and

0-5
Arnie
(-5) * (-5) = (-5)², not -5². Otherwise you'd say the unary operation - can only apply to single numbers, not to expressions such as 5².
GSIS
As written the example given the '-' is an assignment - not an operator.

Thus, operator precedence has no place in the discussion.

The value to be squared has been assigned (the value) of -5. It has not been subtracted from anything (including 0).

-5^2 = (-5)^2 NOT -(5^2)

The question, clearly, is imprecise if basic mathematical notation has been changed in the last 30 years. I seriously suggest that if you see a question in that form on any exam paper you provide BOTH answers - and explain why you believe the question is inappropriate in the exam.
sonam
 Quote: (-5) * (-5) = (-5)², not -5²

We can discus about it. If we have positive and negative numbers then minus is not separated from this number. Minus is part of -5. If we didn't follow this rules then -5*-5 can be whatever, independent when we include each minus in our calculation.

Sonam
ocalhoun
So, basically, the question under dispute is:
Which one of these statements is true:
-5^2=(-5)^2
-or-
-5^2=-(5^2)
Arnie
If you have x² and you want to assign the value -5, you must write (-5)².
kerryworkman
I just got out of an algebra class this last week and I only learned one thing the entire semester. That one thing is that math sucks!!!! No matter how much of it you know, you still make mistakes, in how a rule is applied, in the simplification, in one of the three thousand steps it takes to solve the problem. My teacher was a math genius straight out of lockheed and even he constantly got it wrong. Even if you are right someone else may have a different way of solving it which in turn brings the debate over which is best or even correct. It is true we could not live the lives we do without math, but personally I hate it.
imagefree
 GSIS wrote: The basic problem, here, is a lack of understanding. We are talking about the difference between a negative number (-5), and a mathematical expression (0-5) which does not exist in the original question. Had this expression existed the question would then have been: x = 0-5^2 What is x? If you enter the formula =0-5^2 into Excel the response is, indeed, -25. This is because Excel applies normal operator precedence. However, =-5^2 returns +25. This is because the '-' indicates that the number to be squared IS negative - not that it is to be subtracted from 0. Given the choice I think I'd accept Excel as correct rather than imagefree. Perhaps imagefree would like to report this as a bug in Excel?

Yes it is
imagefree
 ocalhoun wrote: So, basically, the question under dispute is: Which one of these statements is true: -5^2=(-5)^2 -or- -5^2=-(5^2)

The Second one is true, ie -5^2=-(5^2)=-25

There is no other argument.
All the Friends opposing me and my explanation have no proper explanation for what they say. They are just opposing but not providing proper arguments.
Read all the posts in this Thread and see the references provided in this regard. Even i have provided a hirerchy table for better explanation.

Hope you Understand
Arnie
Actually they do have arguments, but they're not correct. Indeed the second one is the only possible option because the - applies to 5² as a whole, because squares have to be executed before unary operators such as -.

GSIS apparently thinks operators can only be stuff like +, -, *, / etc. but those are binary operators. The - that makes a number negative is a unary operator.
 Arnie wrote: Strictly speaking the minus in -5 is a unary operation and the - in 0-5 is a binary operation. On some scientific calculators, they are different keys: the unary is a small - and the binary is bigger.

Wikipedia.
sonam
 Quote: If you have x² and you want to assign the value -5, you must write (-5)².

Ah, jeah I think you are right, brackets are impotrant.

Sonam
zinitine
I'm just finishing up grade 10 this summer, so this is what I just learned:
-5² = -(5*5) -25
(-5)² = (-5)(-5) = 25
ocalhoun
Bah, I'm still of the school of thought that the - in -5 is an assignment of value, not an operator, and is therefore not effected by the order of operations. (The math tutor at my college agrees)

Let me put it this way:
If the - in -5 is an operator, then try this math problem:
simplify: -5
It should be as easy as other problems like these:
simplify: 5*5
simplify: 4-2
simplify: -(2+3)
In those cases, the -,+, and * are operators.
imagefree
 ocalhoun wrote: Bah, I'm still of the school of thought that the - in -5 is an assignment of value, not an operator, and is therefore not effected by the order of operations. (The math tutor at my college agrees) Let me put it this way: If the - in -5 is an operator, then try this math problem: simplify: -5 It should be as easy as other problems like these: simplify: 5*5 simplify: 4-2 simplify: -(2+3) In those cases, the -,+, and * are operators.

Everything in mathematics other than digits are operators, and it depends upon the nature of the operator how does it operate. The operator whom you think an assignment of value is a unary operator and applies to only one value. Its the nature of the operator (-) that it makes the number negative but seriously you have to consider the hirerchy of operators while computing. Following are some operators:
- (Binary Operator)
- (Unay Operator)
+ (Binary)
+(Unary)
Division /
Multiplication X
()
{}
[]
Powers and Roots like Squair root etc.

and obviuosly if we ignore hirerchy at any stage of calculation, the unary operators like -,+,Powers, ()s will start creating problems.

Hope u understand.
Manuel
You are right imagefree!