Square root

Question

https://gmatclub.com/forum/download/file_private.php?id=78866 
If the value of (3-2x) is negative, shouldn't the square of square root of (3-2x) be (-3+2x)?
Why is it automatically considered positive here?

Archit3110 · Answer

Its opening bracket over square
Value under sqrt raised to power square is ((a)^1/2)^2 =a

Posted from my mobile device

Kinshook · Answer

heeeya

Anything within square root should be positive for GMAT, otherwise square root of a negative number is imaginary.
ie.

\sqrt{-1}=i

Which is an imaginary number.

In general

(\sqrt{a})^2 = (a^{\frac{1}{2}})^2 = a^{\frac{1}{2}*2} = a^1 = a

Bunuel · Answer

That question is discussed here: https://gmatclub.com/forum/if-3-2x-1-2- ... 35539.html Hope it helps.

heeeya · Answer

Thank you Kinshook,
But in reality, when the square root is squared, it should come out as an absolute value, doesn't it?
So if the square root is positive, it will stay as it is
But if it is negative, it will be multiplied by (-1), no?

Bunuel · Answer

No.

All numbers on the GMAT are real numbers, so for  \sqrt{x}  to be defined, x must be non-negative. Also, the square root always gives a non-negative result, that is  \sqrt{9}=3 , not 3 and -3.

I think you are mixing this with  \sqrt{x^2}=|x| . Here, x can be negative because under the square root we have x^2, which is always non-negative, not x. As a result, we get |x|, which is also non-negative.

Square root

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Square root

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