Question

What is `4sqrt5 + 2sqrt20`?

Answer 1

The simplified expression is `8sqrt5`.

Explanation:

You have to use these two radical rules to simplify the expression:

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

`sqrt(color(red)a^2)=color(red)a`

To start, factor `20`. Then, things will start to make sense using the above rules:

`color(white)=4sqrt5+2sqrt20`

`=4sqrt5+2sqrt(color(red)2*color(blue)2*color(green)5)`

`=4sqrt5+2sqrt(color(purple)2^2*color(green)5)`

`=4sqrt5+2sqrtcolor(purple)(2^2)*sqrtcolor(green)5`

`=4sqrt5+2*color(purple)2*sqrtcolor(green)5`

`=4sqrt5+4*sqrtcolor(green)5`

`=4sqrt5+4sqrtcolor(green)5`

`=8sqrt5~~17.88854...`

That's as simplified as it gets. Hope this helped!