Question 188729
If the expression is {{{4/(sqrt(5)+sqrt(3))}}} then {{{4/(sqrt(5)+sqrt(3)) = 2*(sqrt(5)-sqrt(3))}}} and you're correct. Good job.



You can simplify the expression by distributing to get {{{2*sqrt(5)-2*sqrt(3)}}}, but that's trivial.



Note:  Using a calculator, we can find that



*[Tex \LARGE \frac{4}{\sqrt{5}+\sqrt{3}} \approx 1.00803433986182]



and



*[Tex \LARGE 2\left(\sqrt{5}-\sqrt{3}\right) \approx 1.00803433986182]



So this shows us that *[Tex \LARGE \frac{4}{\sqrt{5}+\sqrt{3}}=2\left(\sqrt{5}-\sqrt{3}\right)]