Question

How do you simplify `4sqrt(66g^2h^4)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`4sqrt(66g^2h^4) => sqrt(g^2h^4 * 66)`

Now, use this rule for radicals to simplify:

`sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))`

`4sqrt(color(red)(g^2h^4) * color(blue)(66)) => 4(sqrt(color(red)(g^2h^4)) * sqrt(color(blue)(66))) => 4gh^2sqrt(66)`

`66 = 2 xx 3 xx 11` so there is no way to factor it to smaller numbers which are squared numbers.