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Fundamental Radical / Exponents Question

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Fundamental Radical / Exponents Question [#permalink]

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New post 24 Nov 2015, 10:04
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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Re: Fundamental Radical / Exponents Question [#permalink]

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New post 24 Nov 2015, 21:50
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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 ( [16] ) = +/- 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
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Re: Fundamental Radical / Exponents Question [#permalink]

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New post 25 Nov 2015, 01:25
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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Re: Fundamental Radical / Exponents Question [#permalink]

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New post 14 Apr 2018, 21:51
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Re: Fundamental Radical / Exponents Question   [#permalink] 14 Apr 2018, 21:51
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