次の4つの計算問題を解く。 (1) $\sqrt{32} \times \sqrt{2}$ (2) $2\sqrt{27} \times \sqrt{12}$ (3) $7\sqrt{2} \div \sqrt{7}$ (4) $3\sqrt{90} \div \sqrt{15} \div 6\sqrt{2}$

1. 問題の内容

次の4つの計算問題を解く。

(1) $\sqrt{32} \times \sqrt{2}$

(2) $2\sqrt{27} \times \sqrt{12}$

(3) $7\sqrt{2} \div \sqrt{7}$

(4) $3\sqrt{90} \div \sqrt{15} \div 6\sqrt{2}$

2. 解き方の手順

(1) $\sqrt{32} \times \sqrt{2}$

$\sqrt{32 \times 2} = \sqrt{64} = 8$

(2) $2\sqrt{27} \times \sqrt{12}$

$2\sqrt{27 \times 12} = 2\sqrt{324} = 2 \times 18 = 36$

(3) $7\sqrt{2} \div \sqrt{7}$

$\frac{7\sqrt{2}}{\sqrt{7}} = \frac{7\sqrt{2}\sqrt{7}}{\sqrt{7}\sqrt{7}} = \frac{7\sqrt{14}}{7} = \sqrt{14}$

(4) $3\sqrt{90} \div \sqrt{15} \div 6\sqrt{2}$

$3\sqrt{90} \div \sqrt{15} \div 6\sqrt{2} = \frac{3\sqrt{90}}{\sqrt{15} \times 6\sqrt{2}} = \frac{3\sqrt{90}}{6\sqrt{30}} = \frac{3\sqrt{3}\sqrt{30}}{6\sqrt{30}} = \frac{3\sqrt{3}}{6} = \frac{\sqrt{3}}{2}$

3. 最終的な答え

(1) 8

(2) 36

(3) $\sqrt{14}$

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