What is the simplified fourth root of 324?

Answer 1

Since it's hard to type math symbols on the computer, I'll represent the "fourth root" with the symbol ^(1/4).

So your initial problem would look like 324^(1/4).

Got it?

The first thing you must do is factor 324. It's obvious (or should be) that 2 is a factor.

324/2 = 162

2 is also a factor of 162.

162/2 = 81

And of course 81 = 9 * 9 = 3 * 3 * 3 * 3

So the complete factorization of 324 is

324 = 3 * 3 * 3 * 3 * 2 * 2

So . . .

324^(1/4) = 3*(2*2)^(1/4) = 3*4^(1/4)

Thus your final answer would be 3*4^(1/4).