Question

How do you simplify `(2 sqrt(7) + sqrt(3)) times (3 sqrt(7) - sqrt(2))`?

Answer 1

The value is `42-2sqrt(14)+3sqrt(21)-sqrt(6)`

Explanation:

`(2sqrt(7)+sqrt(3))xx(3sqrt(7)-sqrt(2))`
`=6*7-2sqrt(7)sqrt(2)+3sqrt(7)sqrt(3)-sqrt(2)sqrt(3)`
`=42-2sqrt(14)+3sqrt(21)-sqrt(6)`

In these calculations I used the following properties of square roots:

1. `sqrt(a*b)=sqrt(a)*sqrt(b)`

2. `sqrt(a*a)=a`