Question

How do you simplify `2sqrt33 - sqrt30`?

Answer 1

`2sqrt3(sqrt(11) - sqrt(10))`

Explanation:

The key is to factor the numbers under the square roots and try to find a factor that is a perfect square.

For `33`, the factors are `1, 3, 11, 33`. Since none of these are perfect squares, we cannot simplify it.

For `30`, the factors are `1, 3, 5, 6, 10, 30`. Since none of these are perfect squares, we cannot simplify it.

Hence, `2sqrt(33) - sqrt(30)` is already pretty simplified.

There is one thing that you might do to "simplify", but I don't see the benefit.

You could identify that `3` is a common factor of both `30` and `33`. This allows you to factor out a `sqrt3`. You would get:

`2sqrt3(sqrt(11) - sqrt(10))`