Efficiently Solve Roots Problems Without a Calculator

[kenewbie]

Homework Statement

Without using a calculator, find the solution to

$$\sqrt[3]{0.64 * 10^8}$$

The Attempt at a Solution

Well, I figure I want to get everything into powers of 3.

4^3 = 64, but that leaves 100 as the denominator to get 0.64, which does not play well with ^3.

I can split 10^8 into 10^3 * 10^3 * 10^2, but I don't see how that helps since I'm left with 10^2.

I can get to $$100 * \sqrt[3]{0.64 * 10^2}$$ which does give 400 (the correct answer).

So, what am I missing here?

k

 

[kenewbie]

D'oh, finally saw it, sorry.

0.64 * 10^8 = 64 * 10^6, which makes the whole thing come together :)

k