$\sqrt{3}=1.732$、$\sqrt{30}=5.477$の値が与えられたとき、以下の値を求めます。 (1) $\sqrt{300}$ (2) $\sqrt{3000}$ (3) $\sqrt{0.3}$ (4) $\sqrt{30000}$ (5) $\frac{3}{\sqrt{12}}$ (6) $\sqrt{120}$

1. 問題の内容

$\sqrt{3}=1.732$、$\sqrt{30}=5.477$の値が与えられたとき、以下の値を求めます。

(1) $\sqrt{300}$

(2) $\sqrt{3000}$

(3) $\sqrt{0.3}$

(4) $\sqrt{30000}$

(5) $\frac{3}{\sqrt{12}}$

(6) $\sqrt{120}$

2. 解き方の手順

(1) $\sqrt{300}$

$\sqrt{300} = \sqrt{3 \times 100} = \sqrt{3} \times \sqrt{100} = 10\sqrt{3}$

$\sqrt{3}=1.732$より、$\sqrt{300} = 10 \times 1.732 = 17.32$

(2) $\sqrt{3000}$

$\sqrt{3000} = \sqrt{30 \times 100} = \sqrt{30} \times \sqrt{100} = 10\sqrt{30}$

$\sqrt{30}=5.477$より、$\sqrt{3000} = 10 \times 5.477 = 54.77$

(3) $\sqrt{0.3}$

$\sqrt{0.3} = \sqrt{\frac{3}{10}} = \sqrt{\frac{30}{100}} = \frac{\sqrt{30}}{\sqrt{100}} = \frac{\sqrt{30}}{10}$

$\sqrt{30}=5.477$より、$\sqrt{0.3} = \frac{5.477}{10} = 0.5477$

(4) $\sqrt{30000}$

$\sqrt{30000} = \sqrt{3 \times 10000} = \sqrt{3} \times \sqrt{10000} = 100\sqrt{3}$

$\sqrt{3}=1.732$より、$\sqrt{30000} = 100 \times 1.732 = 173.2$

(5) $\frac{3}{\sqrt{12}}$

$\frac{3}{\sqrt{12}} = \frac{3}{\sqrt{4 \times 3}} = \frac{3}{2\sqrt{3}} = \frac{3\sqrt{3}}{2\sqrt{3}\sqrt{3}} = \frac{3\sqrt{3}}{2 \times 3} = \frac{\sqrt{3}}{2}$

$\sqrt{3}=1.732$より、$\frac{3}{\sqrt{12}} = \frac{1.732}{2} = 0.866$

(6) $\sqrt{120}$

$\sqrt{120} = \sqrt{4 \times 30} = \sqrt{4} \times \sqrt{30} = 2\sqrt{30}$

$\sqrt{30}=5.477$より、$\sqrt{120} = 2 \times 5.477 = 10.954$

3. 最終的な答え

(1) $\sqrt{300} = 17.32$

(2) $\sqrt{3000} = 54.77$

(3) $\sqrt{0.3} = 0.5477$

(4) $\sqrt{30000} = 173.2$

(5) $\frac{3}{\sqrt{12}} = 0.866$

(6) $\sqrt{120} = 10.954$