$\sqrt{6} = 2.449$、$\sqrt{60} = 7.746$ として、以下の値を求めなさい。 (1) $\sqrt{600}$ (2) $\sqrt{0.006}$ (3) $\sqrt{150}$ (4) $\sqrt{2.4}$

1. 問題の内容

$\sqrt{6} = 2.449$、$\sqrt{60} = 7.746$ として、以下の値を求めなさい。

(1) $\sqrt{600}$

(2) $\sqrt{0.006}$

(3) $\sqrt{150}$

(4) $\sqrt{2.4}$

2. 解き方の手順

(1) $\sqrt{600} = \sqrt{6 \times 100} = \sqrt{6} \times \sqrt{100} = \sqrt{6} \times 10 = 2.449 \times 10 = 24.49$

(2) $\sqrt{0.006} = \sqrt{\frac{6}{1000}} = \sqrt{\frac{60}{10000}} = \frac{\sqrt{60}}{\sqrt{10000}} = \frac{\sqrt{60}}{100} = \frac{7.746}{100} = 0.07746$

(3) $\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5 \times \sqrt{6} = 5 \times 2.449 = 12.245$

(4) $\sqrt{2.4} = \sqrt{\frac{24}{10}} = \sqrt{\frac{240}{100}} = \frac{\sqrt{240}}{\sqrt{100}} = \frac{\sqrt{4 \times 60}}{10} = \frac{\sqrt{4} \times \sqrt{60}}{10} = \frac{2 \times \sqrt{60}}{10} = \frac{2 \times 7.746}{10} = \frac{15.492}{10} = 1.5492$

3. 最終的な答え

(1) $\sqrt{600} = 24.49$

(2) $\sqrt{0.006} = 0.07746$

(3) $\sqrt{150} = 12.245$

(4) $\sqrt{2.4} = 1.5492$