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

1 Answer
Jun 11, 2018

Answer:

#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#