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

1 Answer
Jun 11, 2018

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