Question

How do you simplify `sqrt(80)`?

Answer 1

If `a, b >= 0` then `sqrt(ab) = sqrt(a)sqrt(b)`
If `a >= 0` then `sqrt(a^2) = a`

Hence `sqrt(80) = sqrt(16*5) = 4sqrt(5)`

Explanation:

`sqrt(80) = sqrt(16*5) = sqrt(4^2*5) = sqrt(4^2)sqrt(5) = 4sqrt(5)`

Note that since `sqrt(81) = sqrt(9^2) = 9` then

`9/4 = sqrt(81)/(sqrt(80)/sqrt(5)) = sqrt(81/80)sqrt(5)` is a useful approximation for `sqrt(5)`.