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

Answer 1

Eva Adamson

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

#(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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Answer 2

Eva Abramson

The value of [5(square root of 5) + 3(square root of 7)] / [4(square root of 7) - 3(square root of 5)] is (5√5 + 3√7) / (4√7 - 3√5).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.