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
Please explain
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Last edited by navdeepbajwa on Tue Nov 10, 2009 10:28 am, edited 2 times in total.
- grockit_jake
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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.
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.
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- grockit_jake
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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 -
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 -
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