Question

What is the square root of `360` divided by `640` ?

Answer 1

`sqrt(360/640) = 3/4`

Explanation:

I think what you want is the simplified form of the square root of `360/640`.

If so then first note that if `a, b > 0` then:

`sqrt(a/b) = sqrt(a)/sqrt(b)`

Also, if `a >= 0` then:

`sqrt(a^2) = a`

So we find:

`sqrt(360/640) = sqrt((2^3*3^2*5)/(2^7*5)) = sqrt(3^2/2^4) = sqrt(3^2)/(sqrt((2^2)^2)) = sqrt(3^2)/sqrt(4^2) = 3/4`

Alternatively:

`sqrt(360/640) = sqrt((36*color(red)(cancel(color(black)(10))))/(64*color(red)(cancel(color(black)(10))))) = sqrt(36/64) = sqrt(36)/sqrt(64) = sqrt(6^2)/sqrt(8^2) = 6/8 = 3/4`