問題
次の式を2重根号を外して簡単にせよ.
解説
- (1) $\sqrt{5+\sqrt{24}}$
- $=\sqrt{5+2\sqrt{6}}=\sqrt{(\sqrt{2}+\sqrt{3})^{2}}=$$\sqrt{2}+\sqrt{3}$
- (2) $\sqrt{11+4\sqrt{6}}$
- $=\sqrt{(\sqrt{8}+\sqrt{3})^{2}}=\sqrt{8}+\sqrt{3}=$$2\sqrt{2}+\sqrt{3}$
- (3) $\sqrt{12-8\sqrt{2}}$
- $=\sqrt{(\sqrt{8}-\sqrt{4})^{2}}=\sqrt{8}-\sqrt{4}=$$2\sqrt{2}-2$
