Question

How do you simplify `5sqrt17+17sqrt5`?

Answer 1

`5sqrt(17)+17sqrt(5)` is already in simplest form.

Explanation:

The numbers `5` and `17` are unrelated primes, so it is not possible to combine their square roots to simplify this expression.

If you wished, you could express it differently as:

`5sqrt(17)+17sqrt(5) = sqrt(5)^2sqrt(17)+sqrt(17)^2sqrt(5)`

`color(white)(5sqrt(17)+17sqrt(5)) = sqrt(5)sqrt(17)(sqrt(5)+sqrt(17))`

`color(white)(5sqrt(17)+17sqrt(5)) = sqrt(85)(sqrt(5)+sqrt(17))`

but I would not call that simpler.