Question

How do you simplify `sqrt32`?

Answer 1

The answer is `4sqrt2`.

Let's decompose `32` in its prime factors :

`32 -: 2 = 16`,
`16 -: 2 = 8`,
`8-:2 = 4`,
`4-:2 = 2`,
`2-:2=1`.

That gives us `32 = 2^5`.

Therefore, `sqrt32 = sqrt(2^5) = sqrt(2*2*2*2*2) = sqrt4 * sqrt4 * sqrt2 = 2*2"sqrt2 = 4sqrt2`.