$\sqrt{2} = 1.414$、$\sqrt{20} = 4.472$ を用いて、$\sqrt{200}$、$\sqrt{2000}$、$\sqrt{0.2}$、$\sqrt{0.02}$ の近似値を求める問題です。

1. 問題の内容

$\sqrt{2} = 1.414$、$\sqrt{20} = 4.472$ を用いて、$\sqrt{200}$、$\sqrt{2000}$、$\sqrt{0.2}$、$\sqrt{0.02}$ の近似値を求める問題です。

2. 解き方の手順

(1) $\sqrt{200}$ の近似値

$\sqrt{200}$ を簡単にすると、

$\sqrt{200} = \sqrt{100 \times 2} = \sqrt{10^2 \times 2} = 10\sqrt{2}$

$\sqrt{2} = 1.414$ を用いると、

$10\sqrt{2} = 10 \times 1.414 = 14.14$

(2) $\sqrt{2000}$ の近似値

$\sqrt{2000}$ を簡単にすると、

$\sqrt{2000} = \sqrt{100 \times 20} = \sqrt{10^2 \times 20} = 10\sqrt{20}$

$\sqrt{20} = 4.472$ を用いると、

$10\sqrt{20} = 10 \times 4.472 = 44.72$

(3) $\sqrt{0.2}$ の近似値

$\sqrt{0.2} = \sqrt{\frac{2}{10}} = \sqrt{\frac{20}{100}} = \frac{\sqrt{20}}{\sqrt{100}} = \frac{\sqrt{20}}{10}$

$\sqrt{20} = 4.472$ を用いると、

$\frac{\sqrt{20}}{10} = \frac{4.472}{10} = 0.4472$

(4) $\sqrt{0.02}$ の近似値

$\sqrt{0.02} = \sqrt{\frac{2}{100}} = \frac{\sqrt{2}}{\sqrt{100}} = \frac{\sqrt{2}}{10}$

$\sqrt{2} = 1.414$ を用いると、

$\frac{\sqrt{2}}{10} = \frac{1.414}{10} = 0.1414$

3. 最終的な答え

(1) $\sqrt{200} = 14.14$

(2) $\sqrt{2000} = 44.72$

(3) $\sqrt{0.2} = 0.4472$

(4) $\sqrt{0.02} = 0.1414$