Question

How do you simplify `sqrt72 * sqrt32`?

Answer 1

The answer is `48`

Explanation:

To multiply square roots, it is easiest to just multiply the radicands (the numbers under the radical sign) and imagine the radical signs away for a minute.
So when we see:
`sqrt75 xx sqrt32` mentally remove the radicands and multiply.
`72 xx 32 = 2,304`

Now, we're going to put the radical sign back on and find the square root:
`sqrt2304 = 48`

Answer 2

`48`

Explanation:

`sqrt72xxsqrt32`

`sqrt72=sqrt(2xx2xx2xx3xx3)`

`sqrt32=sqrt(2xx2xx2xx2xx2)`

Therefore,

`sqrt72xxsqrt32=sqrt(2xx2xx2xx3xx3)xxsqrt(2xx2xx2xx2xx2)`

`= 2xx3xxsqrt2xx2xx2xxsqrt2`

`= 2xx3xx2xx2xx2`

`= 48`

~Hope this helps! :)