Question

How do you simplify `2 sqrt216 + 4sqrt 150`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite the terms within the radicals as:

`2sqrt(36 * 6) + 4sqrt(25 * 6)`

We can use this rule of radicals to simplify the radical terms:

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

`2sqrt(color(red)(36) * color(blue)(6)) + 4sqrt(color(red)(25) * color(blue)(6)) => 2sqrt(color(red)(36))sqrt(color(blue)(6)) + 4sqrt(color(red)(25))sqrt(color(blue)(6)) =>`

`(2 * 6sqrt(6)) + (4 * 5sqrt(6)) => 12sqrt(6) + 20sqrt(6)`

We can now combine like terms:

`12sqrt(6) + 20sqrt(6) => (12 + 20)sqrt(6) =>`

`32sqrt(6)`