与えられた複数の根号を含む数式の計算問題を解き、簡略化します。

はい、承知いたしました。画像にある数学の問題を解きます。

1. 問題の内容

与えられた複数の根号を含む数式の計算問題を解き、簡略化します。

2. 解き方の手順

(10) $\frac{\sqrt{15}}{5\sqrt{10}}$

$\frac{\sqrt{15}}{5\sqrt{10}} = \frac{\sqrt{3}\sqrt{5}}{5\sqrt{2}\sqrt{5}} = \frac{\sqrt{3}}{5\sqrt{2}} = \frac{\sqrt{3}\sqrt{2}}{5\sqrt{2}\sqrt{2}} = \frac{\sqrt{6}}{10}$

(11) $\frac{\sqrt{35}}{3\sqrt{21}}$

$\frac{\sqrt{35}}{3\sqrt{21}} = \frac{\sqrt{5}\sqrt{7}}{3\sqrt{3}\sqrt{7}} = \frac{\sqrt{5}}{3\sqrt{3}} = \frac{\sqrt{5}\sqrt{3}}{3\sqrt{3}\sqrt{3}} = \frac{\sqrt{15}}{9}$

(12) $\frac{\sqrt{20}}{\sqrt{48}}$

$\frac{\sqrt{20}}{\sqrt{48}} = \frac{\sqrt{4 \cdot 5}}{\sqrt{16 \cdot 3}} = \frac{2\sqrt{5}}{4\sqrt{3}} = \frac{\sqrt{5}}{2\sqrt{3}} = \frac{\sqrt{5}\sqrt{3}}{2\sqrt{3}\sqrt{3}} = \frac{\sqrt{15}}{6}$

(13) $\frac{\sqrt{15}}{\sqrt{54}}$

$\frac{\sqrt{15}}{\sqrt{54}} = \frac{\sqrt{3}\sqrt{5}}{\sqrt{9 \cdot 6}} = \frac{\sqrt{3}\sqrt{5}}{3\sqrt{2}\sqrt{3}} = \frac{\sqrt{5}}{3\sqrt{2}} = \frac{\sqrt{5}\sqrt{2}}{3\sqrt{2}\sqrt{2}} = \frac{\sqrt{10}}{6}$

(14) $2\sqrt{\frac{5}{3}}$

$2\sqrt{\frac{5}{3}} = 2\frac{\sqrt{5}}{\sqrt{3}} = 2\frac{\sqrt{5}\sqrt{3}}{\sqrt{3}\sqrt{3}} = 2\frac{\sqrt{15}}{3} = \frac{2\sqrt{15}}{3}$

(15) $4\sqrt{\frac{15}{8}}$

$4\sqrt{\frac{15}{8}} = 4\frac{\sqrt{15}}{\sqrt{8}} = 4\frac{\sqrt{15}}{\sqrt{4 \cdot 2}} = 4\frac{\sqrt{15}}{2\sqrt{2}} = 2\frac{\sqrt{15}}{\sqrt{2}} = 2\frac{\sqrt{15}\sqrt{2}}{\sqrt{2}\sqrt{2}} = 2\frac{\sqrt{30}}{2} = \sqrt{30}$

(16) $\frac{3}{2}\sqrt{\frac{2}{3}}$

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

3. 最終的な答え

(10) $\frac{\sqrt{6}}{10}$

(11) $\frac{\sqrt{15}}{9}$

(12) $\frac{\sqrt{15}}{6}$

(13) $\frac{\sqrt{10}}{6}$

(14) $\frac{2\sqrt{15}}{3}$

(15) $\sqrt{30}$

(16) $\frac{\sqrt{6}}{2}$