What is the Square root 20 - square root 5 + square root 45?

1 Answer
Sep 10, 2015

Answer:

#=color(blue)(4sqrt5#

Explanation:

We first simplify #sqrt20# and #sqrt45#terms by prime factorisation:

#sqrt20 = sqrt(2^2 *5)= color(bluw)(2sqrt5#

#sqrt(45) = sqrt(3^2 *5)=color(blue)(3sqrt5#

The expression can now be written as:

#sqrt 20 -sqrt5 +sqrt45 = color(blue)(2sqrt5 )- sqrt5 +color(blue)(3sqrt5#

#=sqrt5 +3sqrt5#
#=color(blue)(4sqrt5#