How do you rationalize the denominator $(8sqrt2)/(2sqrt5-3sqrt2)$ ?

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Answer 1 · 2015-06-14T22:24:04

Multiply both numerator and denominator by the conjugate $(2sqrt(5)+3sqrt(2))$ to get:

$(8sqrt(2))/(2sqrt(5)-3sqrt(2)) =$

$(8sqrt(2))/(2sqrt(5)-3sqrt(2))$

$=(8sqrt(2))/(2sqrt(5)-3sqrt(2))*(2sqrt(5)+3sqrt(2))/(2sqrt(5)+3sqrt(2))$

$=(8sqrt(2)(2sqrt(5)+3sqrt(2)))/(20-18)$

$=4sqrt(2)(2sqrt(5)+3sqrt(2))$

$=8sqrt(2)sqrt(5)+24$

$=8sqrt(10)+24$

$=8(sqrt(10)+3)$

How do you rationalize the denominator (8sqrt2)/(2sqrt5-3sqrt2)(8sqrt2)/(2sqrt5-3sqrt2)?