Question

What is `3sqrt(8^2)` ?

Answer 1

`3*sqrt(8^2) = 24`

Explanation:

We need to find `3*sqrt(8^2)`. Since squaring and square rooting are inverse functions, they cancel out, leaving just `3*8=24`.

Answer 2

`root(3)(8^2) = 4`

Explanation:

Assuming the intended expression was `root(3)(8^2)`, we find:

`root(3)(8^2) = root(3)((2^3)^2) = root(3)((2^2)^3) = 2^2 = 4`

Answer 3

Assuming `root3(8^2)`, we could also write this as:

`root3(8^2)=8^(2/3)=(2^3)^(2/3)=2^2=4`

This used:

• `rootb(x^a)=x^(a/b)`
• `(x^a)^b=x^(ab)`

And the ability to prime factorize, that is, know that `8=2*2*2=2^3`.