Question

find the fourth root of 124 -32root15

Answer 1

$$\begin{gathered} 124-32\sqrt{15} \\ =64+60-32\sqrt{15} \\ =8^2+{\left(2\sqrt{15}\right)}^2-2\times 8\times 2\sqrt{15} \\ ={\left(8-2\sqrt{15}\right)}^2 \\ ={\left(3+5-2\sqrt{3}\times \sqrt{5}\right)}^2 \\ ={\left({\sqrt{3}}^2+{\sqrt{5}}^2-2\sqrt{3}\times \sqrt{5}\right)}^2 \\ ={\left(\sqrt{5}-\sqrt{3}\right)}^4 \\ Sofourthroot=\left(\sqrt{5}-\sqrt{3}\right) \end{gathered}$$