How do you simplify `sqrt(72/3)`?

`"using the "color(blue)"law of radicals"`

`•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)`

`rArrsqrt(72/3)=sqrt24=sqrt(4xx6)=sqrt4xxsqrt6=2sqrt6`

The goal in simplifying a square root is to divide the terms into their common factors.

This can be done in the following way.

Firstly you divide the radicand to get the simplest term: 24 (`72 / 3`)

Now, you find the common factors of 24.

1. 24 is made up of `6 * 4` or `3 * 8`

6 factors into `2*3` and 4 factors into `2^2` == `2^3 * 3`
3 is a factor of itself and 8 factors into `2^3` == `2^3 * 3`

As you can see, either way you will get to the same result.

Adding this into our radical:
`sqrt(2^3 * 3) = (2^3 * 3)^(1/2) =` exponent rule = `2^(3+(1/2)) * 3^(1/2)`

Rewriting this equation we get:
`2^(5/2) * 3^(1/2)` == `2^2 * (2 ^(1/2)*3^(1/2))`

Applying the square root (or factoring out the exponents)we get:

`sqrt(2^2 * (2 *3)` == `2sqrt(2*3)` == `2sqrt(6)`

dividing under a radical is allowed:

`sqrt(72/3) = sqrt(24) = sqrt(4*6) = sqrt(2^2*6) = 2sqrt6`

`sqrt(72/3)=sqrt24`

`rArr sqrt24=sqrt 4 xx sqrt6`

`rArr2sqrt6`