Question

Find the product.

`(sqrt(2) + 3sqrt(11))(5sqrt(2) - 2sqrt(11))`

Answer 1

Let’s find the product:

`(sqrt(2) + 3sqrt(11))(5sqrt(2) - 2sqrt(11))`

Use distributive property (FOIL method):

Multiply each term:

1. `sqrt(2) xx 5sqrt(2)`

= 5 × 2

= 10

2. `sqrt(2) xx (-2sqrt(11))`

= `-2sqrt(22)`

3. `3sqrt(11) xx 5sqrt(2)`

= `15sqrt(22)`

4. `3sqrt(11) xx (-2sqrt(11))`

= –6 × 11 

= –66

Now combine all:

`10 - 2sqrt(22) + 15sqrt(22) - 66`

Combine like terms:

• Constants: 10 – 66 = –56
• Surds: `-2sqrt(22) + 15sqrt(22) = 13sqrt(22)`