Select all the numbers that are irrational

A)  

D)  

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Explanation:

Choices B and C are rational because we can simplify them to form a fraction of integers.

Any rational number is of the form P/Q where P,Q are integers and Q is nonzero.

So we can rule out choices B and C.

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Choice A on the other hand cannot be written as a fraction of integers. The 5 isn't a perfect square, which makes irrational.

The same can be said about which is roughly equal to 3.14; the decimal digits go on forever without a known pattern.

Choice A and choice D are the two answers.

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If we know the pattern of the decimal digits, then we can turn the decimal number into a fraction of integers

The number -0.777, where the 7s go on forever, converts to the fraction -7/9

That means we rule out choice E.