Question

Tính

\(\sqrt{15+2\sqrt{35}+\sqrt{60}+\sqrt{84}}\)

Answer 1

\(\sqrt{15+2\sqrt{35}+\sqrt{60}+\sqrt{84}}\)

= \(\sqrt{15+2\sqrt{35}+2\sqrt{15}+2\sqrt{21}}\)

= \(\sqrt{3+5+7+2\sqrt{5}\sqrt{7}+2\sqrt{3}\sqrt{5}+2\sqrt{3}\sqrt{7}}\)

= \(\sqrt{\left(\sqrt{3}+\sqrt{5}+\sqrt{7}\right)^2}\)

= \(\sqrt{3}+\sqrt{5}+\sqrt{7}\)

Answer 2

\(\sqrt{15+2\sqrt{35}+\sqrt{60}+\sqrt{84}}\\ =\sqrt{15+2\sqrt{35}+2\sqrt{15}+2\sqrt{21}}\)