Question

Find the product.

`(3sqrt(6) - 5sqrt(2))(4sqrt(6) - 3sqrt(2))`

Answer 1

Let’s find the product:

`(3sqrt(6) - 5sqrt(2))(4sqrt(6) - 3sqrt(2))`

1. `3sqrt(6) xx 4sqrt(6)`

= 12 × 6

= 72

2. `3sqrt(6) xx (-3sqrt(2))`

= `-9sqrt(12)`

3. `-5sqrt(2) xx 4sqrt(6)`

= `-20sqrt(12)`

4. `-5sqrt(2) xx (-3sqrt(2))`

= 15 × 2

= 30

Now simplify:

• `sqrt(12) = sqrt(4 xx 3) = 2sqrt(3)`

• So:

  • `-9sqrt(12) = -18sqrt(3)`

  • `-20sqrt(12) = -40sqrt(3)`

Now combine:

`72 - 18sqrt(3) - 40sqrt(3) + 30`

= `(72 + 30) - 58sqrt(3)`

= `102 - 58sqrt(3)`