Math question- What is a negative number squared?

[BCDisneyFanatic]

Wait, what? I thought you (and others) said -7^2 = -49?

Oops! If you were in my class, you'd be getting a jolly rancher lollipop for catching my mistake

(Hangs head in shame and goes to edit her post )

 

[sam_gordon]

Oops! If you were in my class, you'd be getting a jolly rancher lollipop for catching my mistake

(Hangs head in shame and goes to edit her post )

 

[mhsjax]

Oops! If you were in my class, you'd be getting a jolly rancher lollipop for catching my mistake

(Hangs head in shame and goes to edit her post )

OK so just to be clear, -7 squared is -49? This is what i was taught and in fact I am taking a math class to brush up on this stuff and I think we had one on our last test, and I got it correct. I say it is -49. but (-7) squared is 49. is this correct?

 

[BCDisneyFanatic]

OK so just to be clear, -7 squared is -49? This is what i was taught and in fact I am taking a math class to brush up on this stuff and I think we had one on our last test, and I got it correct. I say it is -49. but (-7) squared is 49. is this correct?

Absolutely

- 7 ^2 = -49

(-7) ^ 2 = +49

I'm about to head into school (I only teach half-days), and my 9s have a test on Powers and exponents this afternoon. I'm hoping they remember, too!!!

 

[EMAW_KSU]

You would put your answers in parenthesis when checking the solution, and you will come up with the correct answer. -7 would be inside parenthesis and therefor become a positive number.

No

-7 in parenthesis is not positive.

 

[EMAW_KSU]

Well, technically there are two values of x for which the equation is valid, and the correct 'answer' should include both values.

There is still only one correct value when -7^2 is simplified, though and that is -49 .

(There are two possible solutions to the opposite operation, though...the square root of +49 is either -7 or +7).

How can -7 be a square root of 49 but -7 squared is not equal to 49?

 

[sam_gordon]

How can -7 be a square root of 49 but -7 squared is not equal to 49?

If you want to square -7, you want to indicate it as (-7). THAT'S where the trouble is coming in.

(-7)^2 = 49
7^2 = 49
-7^2 = -49

I think I have that right.

 

[BCDisneyFanatic]

How can -7 be a square root of 49 but -7 squared is not equal to 49?

The integer negative seven, when squared, does equal +49. Nobody is saying that it doesn't.

What I (and others) have been saying is that, as written, -7^2 does NOT represent 'the integer negative seven squared', it is the negative of the integer positive seven squared. This is the 'accepted' convention and meaning.

Mathematical language is extremely precise, and a set of brackets can often change your answer.

And now I really have to go to work!!!

 

[SandrA9810]

How can -7 be a square root of 49 but -7 squared is not equal to 49?

She is correct. The negative is only "attached" to the seven if it is in parenthesis. so - 7 squared in -49, (-7) squared is 49.

It's been stated for three pages. That's where the issue lies with most people understanding how it still equals a negative number.

I have always put my answer in parenthesis when checking a solution. It's the only way to properly keep things in order. Especially when you have complicated equations.

 

[BCDisneyFanatic]

If you want to square -7, you want to indicate it as (-7). THAT'S where the trouble is coming in.

(-7)^2 = 49
7^2 = 49
-7^2 = -49

I think I have that right.

My work here is done.