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

Question

3700 views around the world

You can reuse this answer
Creative Commons License

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.

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