Question

How do you simplify `5sqrt37`?

Answer 1

`5sqrt37` has no further simplified form possible.

Reasons:

1. `37` itself is not a square number.
2. `37` is a prime number (no other positive divisor except `1` and the number itself) and has no factors which is a square number, so nothing can be taken out of the root.

Answer 2

Manisit is correct that nothing can be taken out of the square root, but you can put something into the square root. Whether you think the result is simpler, I leave to you...

`5sqrt(37) = sqrt(5^2)*sqrt(37) = sqrt(5^2*37) = sqrt(25*37) = sqrt(925)`

...using `sqrt(a)*sqrt(b) = sqrt(a*b)`