What is [5(square root of 5) + 3(square root of 7)] / [ 4(square root of 7) - 3 (square root of 5) ]?

1 Answer
Alan P.
Sep 15, 2015

(159+29sqrt(35))/47
color(white)("XXXXXXXX")assuming I haven't made any arithmetic errors

Explanation:

(5(sqrt(5))+3(sqrt(7)))/(4(sqrt(7))-3(sqrt(5))

Rationalize the denominator by multiplying by the conjugate:

=(5(sqrt(5))+3(sqrt(7)))/(4(sqrt(7))-3(sqrt(5)))xx(4(sqrt(7))+3(sqrt(5)))/(4(sqrt(7))+3(sqrt(5)))

=(20sqrt(35)+15((sqrt(5))^2)+12((sqrt(7))^2)+9sqrt(35))/(16((sqrt(7))^2)-9((sqrt(5))^2))

=(29sqrt(35)+15(5)+12(7))/(16(7)-9(5))

=(29sqrt(35)+75+84)/(112-45)

=(159+29sqrt(35))/47

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