How do you rationalize the denominator and simplify #8/(3-sqrt2)#?

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Answer 1 · 2018-03-02T01:57:43

The answer is #(24+8sqrt2)/7#.

To rationalize the denominator of a fraction, multiply both the numerator and the denominator by the denominator's conjugate.

The conjugate of #3-sqrt2# is #3+sqrt2#

#color(white)=8/(3-sqrt2)#

#=8/((3-sqrt2))color(red)(*((3+sqrt2))/((3+sqrt2)))#

#=(8(3+sqrt2))/((3-sqrt2)(3+sqrt2))#

#=(24+8sqrt2)/(3^2+color(red)cancel(color(black)(3sqrt2-3sqrt2))-(sqrt2)^2)#

#=(24+8sqrt2)/(9-2)#

#=(24+8sqrt2)/7#

This answer is as simplified as possible.