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by navdeepbajwa » Tue Nov 10, 2009 12:49 am
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
Last edited by navdeepbajwa on Tue Nov 10, 2009 10:28 am, edited 2 times in total.
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Source: — Problem Solving |

by grockit_jake » Tue Nov 10, 2009 10:19 am
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.
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com
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Re

by navdeepbajwa » Tue Nov 10, 2009 10:27 am
Thanks for the reply can you please elaborate when we use an expression

Can you please explain my second query too
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by grockit_jake » Tue Nov 10, 2009 10:32 am
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 -
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com
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re

by navdeepbajwa » Tue Nov 10, 2009 2:41 pm
thanks for the clear explanation i got it
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