Question

Which of the following are examples of rational numbers? Select all that apply. ​

Answer 1

3 Answers:

Choice A

Choice D

Choice E

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Step-by-step explanation:

The list of perfect squares is:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ...

If we apply the square root to any of those numbers, then the number is rational.

For example,
`√(25) = 5 = (5)/(1)`

A rational number is any fraction of two integers, where zero is not in the denominator.

Based on this, we can see that choice A represents a rational number because we are summing rational numbers.

More specific proof is to write
`√(4) + √(16) = 2 + 4 = 6 = (6)/(1)` showing it is rational.

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Choice B is ruled out because
`√(5)` is irrational. We cannot write it as a fraction of two integers.

Choice C is ruled out for similar reasoning as choice B. This time
`√(24)` is irrational.

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Choice D is another answer because
`2*√(4) = 2*2 = 4 = (4)/(1)` is rational.

Choice E is another answer as well because
`√(49)*√(81) = 7*9 = 63 = (63)/(1)` is rational.

Choice F is ruled out because
`√(12)` is irrational, which in turn makes
`3√(12)` irrational as well.