How do you rationalize the denominator and simplify #3/(2-sqrt2)#?

1 Answer
Jun 23, 2016

Answer:

#3/(2-sqrt2)=3+3/2sqrt2#

Explanation:

To rationalize the denominator and simplify #3/(2-sqrt2)#, we should multiply numerator and denominator by the conjugate of denominator. As denominator is #2-sqrt2#, its conjugate is #2+sqrt2#.

#3/(2-sqrt2)=(3xx(2+sqrt2))/((2+sqrt2)xx(2-sqrt2))#

= #(6+3sqrt2)/(2^2-2)#

= #(6+3sqrt2)/(4-2)#

= #(6+3sqrt2)/2=3+3/2sqrt2#