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Intern  Joined: 12 Aug 2015
Posts: 3
Schools: Wharton '18 (A)
GMAT 1: 710 Q50 V36 ### Show Tags

The similarity between the two below expressions always causes me doubt. To confirm, is there a fundamental difference between ...

1) sq. root ( [(x^2)] ) - two possible solutions (positive and negative, driven by the even exponent)

2) [(sq. root x)]^2 - one possible solution; even root yields one (positive) solution

Clarification greatly appreciated. Thanks so much!

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SVP  B
Joined: 06 Nov 2014
Posts: 1877

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1
mystseen wrote:
The similarity between the two below expressions always causes me doubt. To confirm, is there a fundamental difference between ...

1) sq. root ( [(x^2)] ) - two possible solutions (positive and negative, driven by the even exponent)

2) [(sq. root x)]^2 - one possible solution; even root yields one (positive) solution

Clarification greatly appreciated. Thanks so much!

The best way to resolve your doubt is by plugging in values.

Assume x = 5
Case 1: sq. root ( [(x^2)] ) = sq. root ( [(4^2)] ) = sq. root (  ) = +/- 4
Case 2: [(sq. root x)]^2 = [(sq. root 4)]^2 = [(2)]^2 = 4

The first case can have negative values also, where as the second case will have positive values only as the last operation is a square
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7597
GMAT 1: 760 Q51 V42 GPA: 3.82

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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

The similarity between the two below expressions always causes me doubt. To confirm, is there a fundamental difference between ...

1) sq. root ( [(x^2)] ) - two possible solutions (positive and negative, driven by the even exponent)

2) [(sq. root x)]^2 - one possible solution; even root yields one (positive) solution

hi! mystseen, this is my explanation...

sq. root(A) is a kind of equation. That means to find the value of sq. root(A) we should find the roots of equation A=x^2. As you can see we have two roots of A=x^2 as long as A is a positive number.(9=x^2 has two roots +-3).

sq. root ( [(x^2)] ), therefore, two values since x^2 is positive.

On the other hand, even if (sq. root x) has possibly two positive and negative values, [(sq. root x)]^2 has only one value since [(sq. root x)]^2 has only positive value. So [(sq. root x)]^2 has only one solution.

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# Fundamental Radical / Exponents Question  