Question

Tinhs

Answer 1

\(\sqrt{8+\sqrt{60}}-\sqrt{9+4\sqrt{5}}\\ =\sqrt{8+\sqrt{4.15}}-\sqrt{9+2.2\sqrt{5}}\\ =\sqrt{8+2\sqrt{15}}-\sqrt{2^2+2.2\sqrt{5}+\sqrt{5^2}}\\ =\sqrt{\sqrt{5^2}+2\sqrt{3}\sqrt{5}+\sqrt{3^2}}-\sqrt{\left(2+\sqrt{5}\right)^2}\\ =\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}-\left(2+\sqrt{5}\right)\\ =\left(\sqrt{5}+\sqrt{3}\right)-\left(2+\sqrt{5}\right)\\ =\sqrt{5}+\sqrt{3}-2-\sqrt{5}\\ =\sqrt{3}-2\)

Answer 2