Question

What is the square root of 80?

Answer 1

`sqrt(80)=4sqrt5`
`color(white)(sqrt(80))~~8.944`

Explanation:

By the properties of square roots:

`sqrt(80) = sqrt(4 xx 20)`
`color(white)(sqrt(80)) = sqrt(4 xx 4 xx 5)`
`color(white)(sqrt(80)) = 4sqrt5`

An approximate decimal answer is 8.944.

Answer 2

`sqrt80=color(blue)(4sqrt5`

Explanation:

Given:

`sqrt80`

Prime factorize `80`.

`sqrt(2xx2xx2xx2xx5)`

Group the same prime factors in pairs.

`sqrt((2xx2)xx(2xx2)xx5)`

Rewrite each pair in exponent form.

`sqrt(2^2xx2^2xx5)`

Apply rule: `sqrt(a^2)=a`

`2xx2sqrt5`

`4sqrt5`