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

2 Answers
Nov 23, 2017

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

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