Question

How do you simplify `sqrt5 + 3sqrt7 - 4sqrt5 - 5sqrt7`?

Answer 1

`-3sqrt5-2sqrt7`

Explanation:

We can rewrite this as

`color(steelblue)(sqrt5-4sqrt5)+color(purple)(3sqrt7-5sqrt7)`

We can factor a `sqrt5` out of the blue terms and a `sqrt7` out of the purple terms. We now have

`color(steelblue)((1-4)sqrt5)-color(purple)((3-5)sqrt7)`

`color(steelblue)(-3sqrt5)color(purple)(-2sqrt7)`

Hope this helps!