Question

How do you simplify `2sqrt20 + 8sqrt45 - sqrt80`?

Answer 1

You first factorise everthing under the root, trying to find squares:

Explanation:

`20=4xx5=2^2xx5`
`45=9xx5=3^2xx5`
`80=16xx5=4^2xx5`

We can take the squares out from underneath the roots
`sqrt20=2sqrt5`
`sqrt45=3sqrt5`
`sqrt80=4sqrt5`

We may add roots with the same argument:

`2sqrt5+3sqrt5+4sqrt5=(2+3+4)sqrt5=9sqrt5`