与えられた15個の平方根の割り算の問題を解く。

1. 問題の内容

与えられた15個の平方根の割り算の問題を解く。

2. 解き方の手順

各問題について、以下の手順で計算する。

(1) $\sqrt{18} \div \sqrt{9} = \sqrt{\frac{18}{9}} = \sqrt{2}$

(2) $\sqrt{42} \div (-\sqrt{6}) = -\sqrt{\frac{42}{6}} = -\sqrt{7}$

(3) $(-\sqrt{56}) \div (-\sqrt{28}) = \sqrt{\frac{56}{28}} = \sqrt{2}$

(4) $\sqrt{8} \div \sqrt{2} = \sqrt{\frac{8}{2}} = \sqrt{4} = 2$

(5) $(-\sqrt{75}) \div \sqrt{3} = -\sqrt{\frac{75}{3}} = -\sqrt{25} = -5$

(6) $\sqrt{54} \div (-\sqrt{6}) = -\sqrt{\frac{54}{6}} = -\sqrt{9} = -3$

(7) $\sqrt{2} \div \sqrt{5} = \sqrt{\frac{2}{5}} = \frac{\sqrt{2}}{\sqrt{5}} = \frac{\sqrt{2} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}} = \frac{\sqrt{10}}{5}$

(8) $\sqrt{3} \div \sqrt{7} = \sqrt{\frac{3}{7}} = \frac{\sqrt{3}}{\sqrt{7}} = \frac{\sqrt{3} \times \sqrt{7}}{\sqrt{7} \times \sqrt{7}} = \frac{\sqrt{21}}{7}$

(9) $\sqrt{17} \div \sqrt{5} = \sqrt{\frac{17}{5}} = \frac{\sqrt{17}}{\sqrt{5}} = \frac{\sqrt{17} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}} = \frac{\sqrt{85}}{5}$

(10) $\frac{\sqrt{35}}{\sqrt{7}} = \sqrt{\frac{35}{7}} = \sqrt{5}$

(11) $\frac{\sqrt{10}}{\sqrt{5}} = \sqrt{\frac{10}{5}} = \sqrt{2}$

(12) $\frac{\sqrt{48}}{\sqrt{8}} = \sqrt{\frac{48}{8}} = \sqrt{6}$

(13) $\frac{\sqrt{56}}{\sqrt{14}} = \sqrt{\frac{56}{14}} = \sqrt{4} = 2$

(14) $\frac{\sqrt{80}}{\sqrt{5}} = \sqrt{\frac{80}{5}} = \sqrt{16} = 4$

(15) $\frac{\sqrt{108}}{\sqrt{3}} = \sqrt{\frac{108}{3}} = \sqrt{36} = 6$

3. 最終的な答え

(1) $\sqrt{2}$

(2) $-\sqrt{7}$

(3) $\sqrt{2}$

(4) 2

(5) -5

(6) -3

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

(8) $\frac{\sqrt{21}}{7}$

(9) $\frac{\sqrt{85}}{5}$

(10) $\sqrt{5}$

(11) $\sqrt{2}$

(12) $\sqrt{6}$

(13) 2

(14) 4

(15) 6