Question

How do you simplify `sqrt80 + sqrt125 - sqrt45 + 2 sqrt20`?

Answer 1

`10sqrt5`

Explanation:

Note that each of the values under the square root sign has 5 as a factor. In addition to this, in each case the other factor is a perfect square.

`sqrt(16 xx 5) + sqrt(25 xx 5) - sqrt(9 xx 5) + 2sqrt(4 xx 5)`

`=4sqrt5 + 5sqrt5 - 3sqrt5 + 2 xx 2sqrt5`

Each term is now given in terms of `sqrt5` and can be simplified to give

`10sqrt5`