Question

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

Answer 1

`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`

Answer 2

`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`