How do you simplify #2 sqrt 20 + 45 sqrt20#?

1 Answer
Mar 4, 2016

Answer:

  • Factorize inside the square roots
  • Use some simple root rules
  • Voilá!

Explanation:

So we have #2sqrt(20) + 45sqrt(20)#

Let's factorize a bit..

#2sqrt(2 * 2 * 5) + 45sqrt(2 * 2 * 5)#

#= 2sqrt(4 * 5) + 45sqrt(4 * 5)#

#= 2sqrt(4) * sqrt(5) + 45 sqrt(4) * sqrt(5)#

#= 2 * 2 sqrt(5) + 45 * 2 sqrt(5) #

#= 4sqrt(5) + 90 sqrt(5)#

#= 94 sqrt(5)#