Question

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

Answer 1

`(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`