Question

Question #b1685

Answer 1

`sqrt8*sqrt20`

`=sqrt(2^2*2)*sqrt(2^2*5)`

`=2sqrt2*2sqrt5`

`=4sqrt(2*5)`

`=4sqrt(10)`

Answer 2

`4sqrt(10)`

Explanation:

Since sometimes students have trouble with exponents, another way to look at this question is to factor the number under the radical where one of the factors is a perfect square.
`sqrt(8)*sqrt(20)=sqrt(4*2)*sqrt(4*5)`
`color(white)(aaaaaaaa)=sqrt(4)sqrt(2)*sqrt(4)sqrt(5)`
`color(white)(aaaaaaaa)=2sqrt(2)*2sqrt(5)`
Then multiply the coefficients together separately and the numbers under the roots separately.
`color(white)(aaaaaaaaa)=(2)(2)sqrt(2*5)`
`color(white)(aaaaaaaaa)=4sqrt(10)`