Question

How do you simplify `(3sqrt5)(2sqrt10)`?

Answer 1

`30sqrt2`

Explanation:

When multiplying coefficients (the whole number) with radicands (the numbers under the square root signs), we multiply them with the other of the same kind.

Hence:

`(3sqrt5)(2sqrt10)`

`=>(3xx2)(sqrt5xxsqrt10)`

The radicands are multiplied under one square root sign.

`=>(6)(sqrt(5xx10))`

`=>6sqrt50`

We can factorise the radicand to simplify it.

`=>6(sqrt(5*5*2))`

Taking out the `5` we get:

`=>6xx5sqrt2`

`=>30sqrt2`