Question

How do you simplify `4sqrt27-sqrt75`?

Answer 1

`4sqrt27-sqrt75=color(blue)(12sqrt3-5sqrt5`

Explanation:

Simplify:

`4sqrt27-sqrt75`

Prime factorize `sqrt27`.

`4sqrt(3^2xx3)-sqrt75`

Apply rule: `sqrt(a^2)=a`

`4xx3sqrt3-sqrt75`

Simplify.

`12sqrt3-sqrt75`

Prime factorize `sqrt75`.

`12sqrt3-sqrt(5^2xx5)`

Apply rule: `sqrt(a^2)=a`

`12sqrt3-5sqrt5`

This is as far as we can go. Since the radicands are not the same, we can not add or subtract.