Question

\(\left(5+2\sqrt{6}\right)\left(49+20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)

Answer 1

\(\left(5+2\sqrt{6}\right)\left(49+20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}=\left(5+2\sqrt{6}\right)^3\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}=\left(\sqrt{3}+\sqrt{2}\right)^6\left(\sqrt{3}-\sqrt{2}\right)=\left(\sqrt{3}+\sqrt{2}\right)^5.1=\left(\sqrt{3}+\sqrt{2}\right)^5\)

Answer 2

$\left(5+2\sqrt{6}\right)\left(49+20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}

=\left(5+2\sqrt{6}\right)^3\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}

=\left(\sqrt{3}+\sqrt{2}\right)^6\left(\sqrt{3}-\sqrt{2}\right)

=\left(\sqrt{3}+\sqrt{2}\right)^5.1

=\left(\sqrt{3}+\sqrt{2}\right)^5$