How do you rationalize the denominator and simplify #6/(3+sqrt3)#?

1 Answer
Aug 30, 2016

Answer:

The answer is #3 - sqrt(3)#.

Explanation:

When rationalizing expressions where the denominators are binomials (two terms), we multiply the entire expression by the conjugate of the denominator.

The conjugate is meant to make a difference of squares when multiplied with its original expression. For example, the conjugate of #a + b # is #a -b#, since #(a + b)(a - b) = a^2 + ab - ab - b^2 = a^2 - b^2#, or a difference of squares.

The conjugate can always be found by switching the middle sign of the denominator. Hence, the conjugate of #3 + sqrt(3)# is #3 - sqrt(3)#.

Let's start the rationalization process.

#=6/(3 + sqrt(3)) xx (3 - sqrt(3))/(3 - sqrt(3))#

#=(18 - 6sqrt(3))/(9 - 3sqrt(3) + 3sqrt(3) - sqrt(9))#

#=(18 - 6sqrt(3))/(9 - 3)#

#=(6(3 - sqrt(3)))/(6)#

#=3 - sqrt(3)#

Hopefully this helps!