$\sqrt{6} = 2.449$、$\sqrt{60} = 7.746$ として、以下の平方根の近似値を求める問題です。 (1) $\sqrt{600}$ (2) $\sqrt{600000}$ (3) $\sqrt{0.6}$ (4) $\sqrt{0.0006}$ (5) $\sqrt{54}$ (6) $\sqrt{15}$

1. 問題の内容

$\sqrt{6} = 2.449$、$\sqrt{60} = 7.746$ として、以下の平方根の近似値を求める問題です。

(1) $\sqrt{600}$

(2) $\sqrt{600000}$

(3) $\sqrt{0.6}$

(4) $\sqrt{0.0006}$

(5) $\sqrt{54}$

(6) $\sqrt{15}$

2. 解き方の手順

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

(2) $\sqrt{600000} = \sqrt{60 \times 10000} = \sqrt{60} \times \sqrt{10000} = 100 \sqrt{60} = 100 \times 7.746 = 774.6$

(3) $\sqrt{0.6} = \sqrt{\frac{6}{10}} = \sqrt{\frac{60}{100}} = \frac{\sqrt{60}}{\sqrt{100}} = \frac{\sqrt{60}}{10} = \frac{7.746}{10} = 0.7746$

(4) $\sqrt{0.0006} = \sqrt{\frac{6}{10000}} = \frac{\sqrt{6}}{\sqrt{10000}} = \frac{\sqrt{6}}{100} = \frac{2.449}{100} = 0.02449$

(5) $\sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3 \sqrt{6} = 3 \times 2.449 = 7.347$

(6) $\sqrt{15} = \sqrt{\frac{15 \times 4}{4}} = \sqrt{\frac{60}{4}} = \frac{\sqrt{60}}{\sqrt{4}} = \frac{\sqrt{60}}{2} = \frac{7.746}{2} = 3.873$

3. 最終的な答え

(1) 24.49

(2) 774.6

(3) 0.7746

(4) 0.02449

(5) 7.347

(6) 3.873