# Square root of a negative number that is squared

• Oct 29th 2008, 02:43 PM
alaricepent
Square root of a negative number that is squared
The value of square root of (√(-9)^2) is:

-9
9i
3
9
none of these

which one is the right answer?
(Worried)
• Oct 29th 2008, 03:26 PM
djmccabie
i would say the ^2 and the √ cancel each other out leaving -9. But as with every reply i post, im not confident lol

I just typed it into the calc and it reads 9. So basically, im useless lol
• Oct 29th 2008, 06:00 PM
superevilcube
Quote:

Originally Posted by alaricepent
The value of square root of (√(-9)^2) is:

-9
9i
3
9
none of these

which one is the right answer?
(Worried)

So this is what I see:

(√(-9)^2)

The square root is over the everything, right? Something like sqrt( (-9)^2)? If so:

The answer is 9. First you square (-9), then you will have sqrt( 81), which is just 9.

However, just to clarify, if you have:

[ √(-9) ]^2, then the answer is just -9 because the square and square root cancels out. I hope that helps.
• Oct 29th 2008, 06:48 PM
Shyam
Quote:

Originally Posted by alaricepent
The value of square root of (√(-9)^2) is:

-9
9i
3
9
none of these

which one is the right answer?
(Worried)

$\displaystyle = {\sqrt {(-9)^2}}$

$\displaystyle = {\sqrt {81}}$

$\displaystyle ={9}$
• Oct 29th 2008, 07:06 PM
kathrynmath
Quote:

Originally Posted by alaricepent
The value of square root of (√(-9)^2) is:

-9
9i
3
9
none of these

which one is the right answer?
(Worried)

(-9)(-9) = 81 since a negative times a negative equals a positive.
square root(81) technically = -9 and 9, but sinc ethis is in elementary and middle school math section, I'm assuming you're only dealing with positive numbers. So, the answer would be 9
• Oct 29th 2008, 09:57 PM
HallsofIvy
Quote:

Originally Posted by kathrynmath
(-9)(-9) = 81 since a negative times a negative equals a positive.
square root(81) technically = -9 and 9, but sinc ethis is in elementary and middle school math section, I'm assuming you're only dealing with positive numbers. So, the answer would be 9

No. $\displaystyle x^2= 81$ for x= 9 or -9 but $\displaystyle \sqrt{81}= 9$, not -9. The square root of a number is defined as the positive root.