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Evaluate the sixth root of 64.
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When it comes to a calculation like the sixth root of 64, we’re really trying to work out what value of 𝑥 to the power of six would give us an answer of 64.
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We should recall that a value like 𝑥 to the sixth power is equivalent to 𝑥 written six times and multiplied.
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So the question is, which value of 𝑥 to the sixth power is 64?
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If we were to try a value of 𝑥 is equal to one, then writing that six times and multiplying would still give us a value of one.
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And that’s not 64.
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We could then try a value of 𝑥 is equal to two.
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We should be careful of course.
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This isn’t the same as working out six times two.
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But instead we would start by thinking about two times two, and that’s four.
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Multiplying four by the next two would give us a value of eight.
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We could then multiply by the next two, giving a value of 16, then multiplied by another two is 32.
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And multiplying 32 by the final two gives us a value of 64.
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There are of course a number of different ways that we can multiply to get the answer of 64.
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For example, when we worked out two times two times two is eight, then we know that we also have another eight in this.
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Multiplying these two eights together would give us an answer of 64.
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What we’ve worked out here is that two to the power of six is 64.
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And that means that the sixth root of 64 is equal to two.
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And that’s the answer to the question.