Question

Упростите выражение:√√5+√21

Answer 1

$\sqrt{5+\sqrt{21}}=\sqrt{\dfrac{10+2\sqrt{21}}{2}}=\dfrac{\sqrt{7+3+2\cdot \sqrt7\cdot \sqrt3}}{\sqrt2}=\dfrac{\sqrt{(\sqrt7+\sqrt3)^2}}{\sqrt2}=\\\\\\=\dfrac{|\sqrt7+\sqrt3|}{\sqrt2}=\dfrac{\sqrt7+\sqrt3}{\sqrt2}\; ;\; \; \; \; \Big(\; \dfrac{\sqrt{14}+\sqrt6}{2}\; \Big)$