ShmoopTube

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And here's an unshmoopy question you may find on an exams somewhere in life...

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Both y and y to the one-third are negative integers.

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Which of the following must also be a negative integer?

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And here are the potential answers...

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All right... we want to find the expression that gives us a negative integer given the

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information provided in the problem.

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In this case, choice A is the correct answer...

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but let's first look at why the other options are incorrect.

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Choice B is asking us to take the square root of a negative number, but that's impossible.

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It's choice C's turn in the hot seat.

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If y is negative, a negative number times a negative number will always be a positive number.

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Choice D's up next.

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y raised to the 2/3 power is the same thing as squaring y raised to the 1/3 power.

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y raised to the 1/3 power is defined as being negative, so squaring it will make it positive.

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Last up, choice E. It's important to know that taking the cubed

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root of y is the same thing as raising y to the 1/3 power.

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By multiplying y by y raised to the 1/3 power, we are multiplying 2 negatives, which gives

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us a positive. Now back to the correct answer, choice A.

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y raised to the 1/3 power is negative, and raising any negative number to an odd power

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will yield another negative number. So bingo --

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A it is.

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