Question

What is 7 over the square root of 27?

Answer 1

`(7 sqrt(3))/9`

Explanation:

Start by writing your expression, which features `7` in the numerator and `sqrt(27)` in the denominator.

`7/(sqrt(27)`

Now, the important thing to realize here is that you can write `27` as

`27 = 9 * 3 = 3 * 3 * 3 = 3""^2 * 3`

This means that the denominator becomes

`sqrt(27) = sqrt(3""^2 * 3) = sqrt(3""^2) * sqrt(3) = 3sqrt(3)`

The expression is now

`7/(3 * sqrt(3))`

Next, you have to rationalize the denominator, which you can do by multiplying the numerator and the denominator by `sqrt(3)`, to get

`(7 * sqrt(3))/(3 * underbrace(sqrt(3) * sqrt(3))_(color(blue)("=3))) = (7 * sqrt(3))/(3 * color(blue)(3)) = color(green)((7 sqrt(3))/9)`