How do you rationalize the denominator and simplify #(15+3sqrt3)/(7+sqrt8)#?

1 Answer
Jun 18, 2017

Answer:

See a solution process below:

Explanation:

To rationalize the denominator, multiply the fraction by #1# in the form of: #(7 - sqrt(8))/(7 - sqrt(8))#:

#(7 - sqrt(8))/(7 - sqrt(8)) xx (15 + 3sqrt(3))/(7 + sqrt(8)) =>#

#((7 * 15) + (7 * 3sqrt(3)) - 15sqrt(8) - 3sqrt(8)sqrt(3))/((7 * 7) + 7sqrt(8) - 7sqrt(8) - (sqrt(8))^2) =>#

#(105 + 21sqrt(3) - 15sqrt(8) - 3sqrt(8 * 3))/(49 + (7sqrt(8) - 7sqrt(8)) - 8) =>#

#(105 + 21sqrt(3) - 15sqrt(8) - 3sqrt(24))/41 =>#

#(105 + 21sqrt(3) - 15sqrt(8) - 3sqrt(4 * 6))/41 =>#

#(105 + 21sqrt(3) - 15sqrt(8) - 3sqrt(4)sqrt(6))/41 =>#

#(105 + 21sqrt(3) - 15sqrt(8) - (3 * 2sqrt(6)))/41 =>#

#(105 + 21sqrt(3) - 15sqrt(8) - 6sqrt(6))/41#