How do you simplify #2sqrt20-sqrt20+3sqrt20-2sqrt45#?

2 Answers
Nov 23, 2017

Answer:

#2sqrt20-sqrt20+3sqrt20-2sqrt45=2sqrt5#

Explanation:

#2sqrt20-sqrt20+3sqrt20-2sqrt45#

= #sqrt20(2-1+3)-2sqrt(3xx3xx5)#

= #sqrt(color(red)(2xx2)xx5)xx4-2sqrt(color(red)(3xx3)xx5)#

= #color(red)2xx4xxsqrt5-color(red)3xx2xxsqrt5#

= #8sqrt5-6sqrt5#

= #(8-6)sqrt5#

= #2sqrt5#

Nov 23, 2017

Answer:

#2sqrt5#

Explanation:

Simplify
#2sqrt20 - sqrt20 + 3sqrt20 - 2sqrt45#

1) Combine like terms
Combine all the coefficients of the #sqrt20# terms
#4sqrt20 - 2sqrt45#

2) Factor to get perfect squares
#4sqrt(2^2*5) - 2sqrt(3^2*5)#

3) Find the square roots, but leave the 5s inside
#(2*4)sqrt5 - (3*2)sqrt5#

This is the same as
#8sqrt5 - 6sqrt5#

4) Combine like terms
#2sqrt5 larr# answer

Answer:
Simplified, the expression is #2sqrt5#