与えられた4つの式をそれぞれ計算し、簡単にします。 (1) $\sqrt{2}\sqrt{3}$ (2) $\sqrt{2\sqrt{8}}$ (3) $\frac{\sqrt{6}}{\sqrt{3}}$ (4) $\frac{\sqrt{24}}{\sqrt{2}}$

1. 問題の内容

与えられた4つの式をそれぞれ計算し、簡単にします。

(1) $\sqrt{2}\sqrt{3}$

(2) $\sqrt{2\sqrt{8}}$

(3) $\frac{\sqrt{6}}{\sqrt{3}}$

(4) $\frac{\sqrt{24}}{\sqrt{2}}$

2. 解き方の手順

(1) $\sqrt{2}\sqrt{3} = \sqrt{2 \times 3} = \sqrt{6}$

(2) $\sqrt{2\sqrt{8}} = \sqrt{2 \times \sqrt{4 \times 2}} = \sqrt{2 \times 2\sqrt{2}} = \sqrt{4\sqrt{2}} = \sqrt{\sqrt{16 \times 2}} = \sqrt{\sqrt{32}} = (32)^{\frac{1}{4}} = (2^5)^{\frac{1}{4}} = 2^{\frac{5}{4}} = 2\sqrt[4]{2}$

もしくは、 $\sqrt{2\sqrt{8}} = \sqrt{2\sqrt{8}} = \sqrt{\sqrt{4}\sqrt{8}} = \sqrt{\sqrt{32}} = \sqrt[4]{32} = \sqrt[4]{16\times2} = \sqrt[4]{2^4\times2} = 2\sqrt[4]{2}$

(3) $\frac{\sqrt{6}}{\sqrt{3}} = \sqrt{\frac{6}{3}} = \sqrt{2}$

(4) $\frac{\sqrt{24}}{\sqrt{2}} = \sqrt{\frac{24}{2}} = \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$

3. 最終的な答え

(1) $\sqrt{6}$

(2) $2\sqrt[4]{2}$

(3) $\sqrt{2}$

(4) $2\sqrt{3}$