ShmoopTube

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Here's an unshmoopy question you'll find on an exam somewhere in life...

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Calculate the square root of 32 times the square root of 8.

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And here are the potential answers...

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OK, so this question is really all about factors

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-- can we recognize and use them?

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We'll rarely be asked to calculate a square root that doesn't come out even on a test like this...

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...so if we feel like we've been backed into that corner of actually having to calculate it...

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...we may have messed up somewhere upstream.

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That's not to say they won't ever throw a weird one in there,

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but... it's just something to keep in mind.

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So, in this case we have to think about the factors

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of 32... 2 and 16 and 4 and 8.

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First we have the square root of 32. What perfect squares go into 32 evenly?

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Well, 4 does... but the bigger the better, in this case anyway...

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16 times 2 equals 32, and 16 is 4 squared.

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So we can rewrite this as the square root of 16 times 2, then we can pull out a 4 to

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make it 4 square root of 2.

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Next on the docket is the square root of 8. Now 4 is the best we can do.

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The square root of 4 times 2 can be rewritten as 2 square root of 2.

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When we multiply these two together, we get 4 times 2 is 8...

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...and then square root of 2 times square root of 2 is... 2.

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Multiply those two numbers together, and we're left with 16...

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So the answer C.

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As in, "Calculating villains."

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