Question

What is the product (in simplest radical form) of the square route of 6 and the square root of 15?

Answer 1

`sqrt(6)*sqrt(15) = 3sqrt(10)`

Explanation:

By radical laws, `sqrt(a) * sqrt(b) = sqrt(ab)`.

Using this law:
`sqrt(6)*sqrt(15)`
`=sqrt(90)`

`sqrt(90)` has `9`, a perfect square, as one of its factors, so it can be simplified.
`sqrt(90)`
`=sqrt(9*10)`
`=sqrt(9)*sqrt(10)`
`=3sqrt(10)`