Question

How do you find the square root of 320?

Answer 1

`8*sqrt5`

Explanation:

I don't know either,
so let's break it down into pieces, shall we?

We have:
`sqrt320`
The only thing that involves 32 in my mind is `4*8` or `2*16`, and so we notice that `320=2*160` or `4*80` or `16*20` or `8*40`, etc...

Let's try with `4*80`:

`sqrt320=sqrt(4*80)`
At this point, it is good to remember the rule:
`sqrt(a*b)=sqrt(a)*sqrt(b)`
so that
`sqrt320=sqrt(4*80)`
`=sqrt(4)*sqrt80`
`=2*sqrt80`

Then you see that `80=4*20`, so:

`sqrt320=2*sqrt80`
`=2*sqrt(4*20)`
`=2*sqrt(4)*sqrt(20)`
`=2*2*sqrt(20)=4*sqrt20`

Again you see that `20=4*5`, so:
`sqrt320=4*sqrt20`
`=4*sqrt(4*5)`
`=4*sqrt4*sqrt5`
`=4*2*sqrt5`
`=8*sqrt5`