How do you rationalize the denominator and simplify $(4sqrt5)/(3sqrt5+2sqrt2)$ ?

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Answer 1 · 2017-05-02T11:40:04

$1/37( 60-8sqrt10)$

To rationalize the denominator multiply by $(3sqrt5-2sqrt2)$ in both numerator and denominator. we get ,

$((4sqrt5)* (3sqrt5-2sqrt2))/((3sqrt5+2sqrt2)*(3sqrt5-2sqrt2)$

$=(12*5 -8*sqrt10)/((3sqrt5)^2- (2sqrt2)^2) = (60-8sqrt10)/(45-8)$

$= (60-8sqrt10)/37 =1/37( 60-8sqrt10)$ [Ans]

Answer 2 · 2017-05-02T12:05:09

we can multiply the fraction by 1 to rationalise the denominator

$(4sqrt5)/(3sqrt5 + 2sqrt2)$ $times (3sqrt5 - 2sqrt2)/(3sqrt5 - 2sqrt2)$

This gives $(60 - 8sqrt10)/(45 - 8)$

i think the remaining workings should be quite easy to complete

How do you rationalize the denominator and simplify (4sqrt5)/(3sqrt5+2sqrt2)(4sqrt5)/(3sqrt5+2sqrt2)?