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

1 Answer
Feb 21, 2016

Answer:

#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#