Question

How do you simplify `sqrt 20 - sqrt 5 + sqrt 45`?

Answer 1

`4sqrt5`

Explanation:

Attempt to rewrite all the radicals in terms of `sqrt5`

consider the factors of 20 - ± ( 1,2,4,5,10,20 )
We want 4 and 5.

since `sqrt20 = sqrt(4xx5) = sqrt4 xxsqrt5 = 2sqrt5`

[ making use of `sqrtaxxsqrtb = sqrtab hArr sqrtab = sqrta xx sqrtb`]

now consider the factors of 45 - ± (1,3,5,9,15,45 )
We want 9 and 5.

since `sqrt45 = sqrt(9xx5) = sqrt9xxsqrt5 =3sqrt5`

`rArrsqrt20-sqrt5+sqrt45 = 2sqrt5 - sqrt5 + 3sqrt5 = 4sqrt5`