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mystseen
Joined: 12 Aug 2015
Last visit: 17 Jun 2016
Posts: 3
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Schools: Wharton '18 (A)
GMAT 1: 710 Q50 V36
24 Nov 2015, 10:04
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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!
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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Hi there,
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24 Nov 2015, 21:50
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mystseen
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
25 Nov 2015, 01:25
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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.
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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THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
