Question

How do you solve `(3\sqrt{15})(7\sqrt{18})?`

Answer 1

`63*sqrt(30)`

Explanation:

we have `sqrt(15)=sqrt(3*5)`
`sqrt(18)=sqrt(3*6)`
Multiplying
`21*3*sqrt(5)*sqrt(6)=63*sqrt(30)`

Answer 2

`3 sqrt(15)*7 sqrt(18) = 63sqrt (30)`

Explanation:

When multiplying two numbers that are made up of a natural number and a root, like `m sqrt(u)` and `n sqrt(v)`, I would follow these steps:

Take `uv` and factorise to see if there is any square factore in `uv`, so it can be written `uv = az^2`
If it is, then `mn sqrt (uv) = mn sqrt (az^2)=mnz sqrt a`

Your answer, then, is `mnz sqrt a`

In this case:
`15*18=(3*5)(2*3^2)=2*3*5*3^2`

Therefore
`3 sqrt(15)*7 sqrt(18) = 3*7 sqrt (2*3*5*3^2)`
=`3*7*3 sqrt (2*3*5)=63sqrt (30)`