Question

How do you simplify `sqrt33-sqrt9`?

Answer 1

Find what is common in the 2 expressions, then factor it out to get to
`sqrt(3) * (sqrt(11)-sqrt(3))`

Explanation:

When we look to "simplify", most times we are looking to combine the terms in a different way than the one presented.

Take this question for example - we want to find a way to combine the two square roots into one expression. To do that, we need to find what is common about them.

`sqrt(33) - sqrt(9)`

let's break down the 33 and 9 into they're respective factors

`sqrt(11 * 3) - sqrt (3 * 3)`

and I can express this in a different way

`(sqrt(11) * sqrt(3)) - (sqrt(3)*sqrt(3))`

Each expression has a `sqrt(3)`, so let's factor that out

`sqrt(3) * (sqrt(11)-sqrt(3))`

And that is the final answer (remember that `sqrt(11)` and `sqrt(3)` are different numbers, so can't simply be subtracted to get `sqrt(8)`)