How do you simplify 4√5 - 2√45?

1 Answer
Stefan V.
Oct 9, 2015

#-2sqrt(5)#

Explanation:

Your starting expression looks like this

#4sqrt(5) - 2sqrt(45)#

Notice that you can write #45# as

#45 = 3 * 15 = 3 * 3 * 5 = 3^2 * 5#

This means that you have

#4sqrt(5) - 2sqrt(3^2 * 5) = 4sqrt(5) - 2 * sqrt(3^2) * sqrt(5)#

#=4sqrt(5) - 2 * 3sqrt(5)#

#= 4sqrt(5) - 6sqrt(5)#

#= sqrt(5) * (4 - 6)#

#= color(green)(-2sqrt(5))#

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