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Column A x = 1/9 Column B     0

Column A Column B
Image 0

(A) Column A is larger
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set S: Exponents & Roots

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Posted: 09/12/2012 06:27
Why is the answer not d? The square root of 1/9 is 1/3 and -1/3. The former would result in column a being bigger, but the later means column b is bigger. Why is the negative root ignored?
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Posted: 09/12/2012 13:50
Lacey, the square root of 1/9 is only 1/3; it doesn't include -1/3.

This is a common mistake that people make. If you are solving for x^2 - 1/9 = 0, that's a different problem, because you can factor out the left hand side to be (x-1/3)(x+1/3) = 0, so that you have two solutions to the problem.

x^2 = 1/9 and x = √1/9 are not the same equations. The first has 2 solutions. The second only has 1 solution. Square roots are always positive.
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