Question

`sqrt(45) - 4sqrt(5) + sqrt(20)` when simplified is ______.

Options

• `-3sqrt(5)`

• `5sqrt(5)`

• `-sqrt(5)`

• `sqrt(5)`

Answer 1

`sqrt(45) - 4sqrt(5) + sqrt(20)` when simplified is `underlinebb(sqrt(5))`.

Explanation:

Let’s simplify each term:

`sqrt(45)`

= `sqrt(9 xx 5)`

= `3sqrt(5)`

Remains as is `-4sqrt(5)`

`sqrt(20)`

= `sqrt(4 xx 5)`

= `2sqrt(5)`

Now combine:

`sqrt(45) - 4sqrt(5) + sqrt(20)`

= `3sqrt(5) - 4sqrt(5) + 2sqrt(5)`

= `(3 - 4 + 2)sqrt(5)`

= `1sqrt(5)`

= `sqrt(5)`