Question

How do you simplify `(18+sqrt567)/9`?

Answer 1

`2 + sqrt7`

Explanation:

Begin by simplifying the radical, and making any squares possible inside the radical.

`(18 + sqrt567)/9` `rArr (18 + sqrt(3^2 * 3^2 * 7))/9`

Now take the squares out and multiply their roots outside the radical:

`(18 + sqrt(3^2 * 3^2 * 7))/9 rArr` `(18 + (3 * 3)sqrt7)/9` `rArr (18 + 9sqrt7)/9`

Now simplify the top and bottom of the expression by canceling out `9`:

`(stackrel2cancel18 + stackrel1cancel9sqrt7)/cancel9_1` `rArr (2 + 1sqrt7)/1 rArr 2 + sqrt7`