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

##### 1 Answer

Feb 21, 2016

#### 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#