Problem Solving

I read that in Official GMAT 12th edition
1)(x^2)^1/2 denotes the non negative square root of x^2, and so (x^2)^1/2=abs x

Can anyone please explain this if x=3 then x^2=9 and root of x has two values -3 and 3 then how can be root of x abs 3 and not +3 and -3

2)Also x^1/2 denotes the positive number whose square is x again the same question why cannot x has both + and - values

For some reason, mathematicians made a decision on this back in the 1400s.

When you have a square root of a number that is not in an equation, then you only take the positive root. For example:

sqrt(9) equals 3 only

9 = x^2
x = +/- 3

The distinction is if you are solving an EQUATION for distinct roots. (In this case +/- 3 are both solutions.) In an EXPRESSION, you only use the positive root.

Honestly, this doesn't come up that often on the GMAT, but it's confusing nonetheless.

Thanks for the reply can you please elaborate when we use an expression

Can you please explain my second query too

An expression is 1 side of an equation. so:

4*sqrt(16) + 6 = x

would convert to

4*4 + 6 = x

NOT
4* (+/-4) + 6 = x

for query 2, the answer is the same. when you take the square root of a number in an expression, you dont consider the -

thanks for the clear explanation i got it