Question

What is the Square root 20 - square root 5 + square root 45?

Answer 1

`=color(blue)(4sqrt5`

Explanation:

We first simplify `sqrt20` and `sqrt45`terms by prime factorisation:

`sqrt20 = sqrt(2^2 *5)= color(bluw)(2sqrt5`

`sqrt(45) = sqrt(3^2 *5)=color(blue)(3sqrt5`

The expression can now be written as:

`sqrt 20 -sqrt5 +sqrt45 = color(blue)(2sqrt5 )- sqrt5 +color(blue)(3sqrt5`

`=sqrt5 +3sqrt5`
`=color(blue)(4sqrt5`