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