Rationalize the denominator. (Simplify your answer completely.)

Question

Rationalize the denominator. (Simplify your answer completely.)

 

 

((square root of 6) + (square root of 5)) / ((square root of 6) - (square root of 5))

Answer 1

The best was to do this is to remember the rule about the difference between two sqares:

 

a² - b² = (a + b) (a - b)

 

So you can get rid of the square roots in the denominator by multiplying it by √6 + √5 -- as long as you multiply the numerator by the same amount.

 

So that would give you the following:

 

(√6 + √5) / (√6 - √5) =

[ (√6 + √5) (√6 + √5) ] / [(√6 + √5) (√6 - √5) ] =

(√6 + √5) ² / (√6² - √5²) = 

(6 + 5 + 2 √6 √5) / = (6 - 5) =

(11 + 2√30) / 1 =

11 + 2√30