How do you rationalize the denominator $(8sqrt2)/(sqrt20-sqrt18)$ ?

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Answer 1 · 2015-05-27T13:22:44

To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator.

$(8sqrt(2))/(sqrt(20)-sqrt(18))$

$= (8sqrt(2))/(sqrt(20)-sqrt(18))* (sqrt(20)+sqrt(18))/(sqrt(20)+sqrt(18))$

$= (8sqrt(40)+8sqrt(36))/(20-18)$

$= (8(2sqrt(10)+6))/2$

$= 24 + 8sqrt(10)$

How do you rationalize the denominator (8sqrt2)/(sqrt20-sqrt18)(8sqrt2)/(sqrt20-sqrt18)?