Question

How do you simplify `4\sqrt{3}+2\sqrt{12}`?

Answer 1

`4sqrt3+2sqrt12=color(blue)(8sqrt3`

Explanation:

Simplify:

`4sqrt3+2sqrt12`

We can only add or subtract numbers with radicals if the radicals are the same.

Prime factorize `sqrt12`.

`4sqrt3+2sqrt(2xx2xx3)`

Write the factorization in exponent form.

`4sqrt3+2sqrt(2^2xx3)`

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

`4sqrt3+2xx2sqrt3`

Simplify `2xx2` to `4`.

`4sqrt3+4sqrt3`

Simplify.

`8sqrt3`