ISEE Word Problems Question 271: Answer and Explanation
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Question: 271
5. If x is the square root of a number that is not a perfect square, y is the square root of a different number that is not a perfect square, and neither x nor y is a factor of the other, which one of the following could be a rational number?
- A.
- B.
- C.
- D.
Correct Answer: C
Explanation:
C
A rational number can be expressed as a fraction. The square root of a number that is not a perfect square is irrational. The expression in choice (C) can be rational because squaring the square root of a number yields that number. Thus both x2 and y2 will be rational, so the quotient of those numbers will be rational.
Plug in values for x and y following the restriction, such as x = 
and y = 
. These numbers are both irrational, as they cannot be expressed as a fraction. Substitute these numbers into each answer choices to determine when the expression can be expressed as a fraction. Only choice (C) can.