Question

Rationalize the denominator 5√3+3√5 / 5√3- 3√5​

Answer 1

`((5\, √(3) +3\,√(5))^2 )/(30 )`

Explanation:

We recall that in order to rationalize this type of denominator, we can use the multiplication (in numerator and denominator) by the denominator's conjugate:

`(5\, √(3) +3\,√(5) )/(5\, √(3) -3\,√(5) ) =(5\, √(3) +3\,√(5) )/(5\, √(3) -3\,√(5) )*(5\, √(3) +3\,√(5) )/(5\, √(3) +3\,√(5) )=\\=((5\, √(3) +3\,√(5))^2 )/((5\, √(3) )^2-(3\,√(5))^2 )=((5\, √(3) +3\,√(5))^2 )/((25*3)-(9*5) )=\\=((5\, √(3) +3\,√(5))^2 )/(30 )`