与えられた6つの計算問題を解く。

1. 問題の内容

与えられた6つの計算問題を解く。

2. 解き方の手順

(1) $\sqrt{6} \times \sqrt{2} \times \sqrt{12}$

$\sqrt{6} \times \sqrt{2} = \sqrt{12}$

$\sqrt{12} \times \sqrt{12} = 12$

(2) $(-\sqrt{14}) \div \sqrt{21} \times (-\sqrt{48})$

$(-\sqrt{14}) \div \sqrt{21} = -\frac{\sqrt{14}}{\sqrt{21}} = -\sqrt{\frac{14}{21}} = -\sqrt{\frac{2}{3}}$

$-\sqrt{\frac{2}{3}} \times (-\sqrt{48}) = \sqrt{\frac{2}{3} \times 48} = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$

(3) $2\sqrt{6} \div 3\sqrt{3} \times 6\sqrt{2}$

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

$\frac{2}{3}\sqrt{2} \times 6\sqrt{2} = \frac{2}{3} \times 6 \times \sqrt{2} \times \sqrt{2} = \frac{2}{3} \times 6 \times 2 = 8$

(4) $\sqrt{24} \div \sqrt{3} \div (-\sqrt{8})$

$\sqrt{24} \div \sqrt{3} = \frac{\sqrt{24}}{\sqrt{3}} = \sqrt{\frac{24}{3}} = \sqrt{8}$

$\sqrt{8} \div (-\sqrt{8}) = \frac{\sqrt{8}}{-\sqrt{8}} = -1$

(5) $(-5\sqrt{2}) \times \sqrt{8} \div (-\sqrt{20})$

$(-5\sqrt{2}) \times \sqrt{8} = -5\sqrt{2 \times 8} = -5\sqrt{16} = -5 \times 4 = -20$

$-20 \div (-\sqrt{20}) = \frac{-20}{-\sqrt{20}} = \frac{20}{\sqrt{20}} = \frac{20}{\sqrt{4 \times 5}} = \frac{20}{2\sqrt{5}} = \frac{10}{\sqrt{5}} = \frac{10\sqrt{5}}{5} = 2\sqrt{5}$

(6) $2\sqrt{18} \div (-\sqrt{32}) \times \sqrt{5}$

$2\sqrt{18} = 2\sqrt{9 \times 2} = 2 \times 3\sqrt{2} = 6\sqrt{2}$

$-\sqrt{32} = -\sqrt{16 \times 2} = -4\sqrt{2}$

$6\sqrt{2} \div (-4\sqrt{2}) = \frac{6\sqrt{2}}{-4\sqrt{2}} = -\frac{6}{4} = -\frac{3}{2}$

$-\frac{3}{2} \times \sqrt{5} = -\frac{3\sqrt{5}}{2}$

3. 最終的な答え

(1) 12

(2) $4\sqrt{2}$

(3) 8

(4) -1

(5) $2\sqrt{5}$

(6) $-\frac{3\sqrt{5}}{2}$