ShmoopTube

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Here’s your shmoop du jour, brought to you by the square root symbol.

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Not to be confused with the square root beer symbol.

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If a = -64 and b = 64, which of the following are not real numbers?

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And here are the potential answers…

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Okay, so we know that a is -64, and b is 64.

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First off, we can substitute the values for a and b.

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The first choice becomes the square root of -64.

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The second becomes the square root of 64, the third becomes the cube root of -64, and

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the fourth becomes the cube root of 64. Now, which of these are not real numbers?

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Remember that a real number is something that exists on a number line.

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That includes natural numbers, integers, and rational numbers.

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What it doesn’t include is imaginary numbers. We get imaginary numbers when we try to take

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an even root of a negative number.

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If we look at option 1, it looks like we’re trying to take the square root of negative 64.

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Well it's imaginary number, since no number squared can equal negative 64.

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Which means option 1 is not a real number.

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Roman numeral 2 is the square root of 64. Well… that’s easy. It’s just 8.

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8 falls within the category of integer, which is a real number.

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Option 3 is the cube root of -64.

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Even though we’re taking the root of a negative number, this number does exists.

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In fact, the cube root of -64 is just negative 4.

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Finally, the cube root of 64.

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The cube root of 64 is, in fact, 4. Choices 2, 3 and 4 all exist.

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However, option number 1 is not a real number.

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Our answer is (A).

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