Question

How do you simplify `sqrt84 * sqrt28`?

Answer 1

`sqrt(84)*sqrt(28)=sqrt(28^2*3)=28sqrt(3)`

Explanation:

Here's a factor tree for `28`:

`color(white)(0000)28`
`color(white)(000)"/"color(white)(00)"\"`
`color(white)(00)2color(white)(000)14`
`color(white)(00000)"/"color(white)(00)"\"`
`color(white)(0000)2color(white)(0000)7`

So: `28 = 2^2*7`

`color(white)()`
Here's a factor tree for `84`:

`color(white)(0000)84`
`color(white)(000)"/"color(white)(00)"\"`
`color(white)(00)2color(white)(000)42`
`color(white)(00000)"/"color(white)(00)"\"`
`color(white)(0000)2color(white)(000)21`
`color(white)(0000000)"/"color(white)(00)"\"`
`color(white)(000000)3color(white)(0000)7`

So: `84 = 2^2*3*7 = 28*3`

`color(white)()`
So:

`sqrt(84)*sqrt(28)=sqrt(84*28)=sqrt(28^2*3)=28sqrt(3)`