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

1 Answer
Sep 15, 2015

Answer:

#(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#