Please explain

[navdeepbajwa]

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

[grockit_jake]

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.

[navdeepbajwa]

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

Can you please explain my second query too

[grockit_jake]

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 -

[navdeepbajwa]

thanks for the clear explanation i got it