ShmoopTube

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And here's your shmoop du jour.

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The expression... the square root of 64 x to the 8th times y to the 4th times z squared...

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is equal to... what?

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And here are the potential answers...

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Before we spoil the ending, hit pause right now and solve it yourself.

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OK, this question is testing our basic ability to root.

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Uh, no, this kind of root. Square kinds.

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And it really tests one thing -- whether we realize that when exponents

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are squared rooted, they are halved.

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That is, the square root of x to the 100th power is x to the 50th power.

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We can rewrite our original equation this way:

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Hopefully we know right off the bat that the square root of 64 is 8.

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And note that immediately we can cross off C and D as choices in the answer set.

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Nice. We've got our chances down to a nice, manageable 50-50 shot here.

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So then we take the square root of x to the 8th and we get x to the 4th...

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y to the 4th becomes y squared and z squared becomes just z.

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And the answer is A. Done. Go team.

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