Question

sqrt(97+56*sqrt(3))/sqrt(7+4*sqrt(3))*sqrt(7-4sqrt(3))

Answer 1

$\frac{\sqrt{97+56\sqrt{3} } }{\sqrt{7+4\sqrt{3} }*\sqrt{7-4\sqrt{3} }} =\frac{\sqrt{49+56\sqrt{3}+48 } }{\sqrt{7+4\sqrt{3} }*\sqrt{7-4\sqrt{3}}}=\frac{\sqrt{(7+4\sqrt{3})^{2}} }{\sqrt{(7+4\sqrt{3})(7-4\sqrt{3})}}=\frac{7+4\sqrt{3} }{\sqrt{49-48} } =7+4\sqrt{3}$