## 問題の内容

## 問題の内容

$\sqrt{7} = 2.646$ と $\sqrt{70} = 8.367$ が与えられたとき、以下の値を求めなさい。

1. $\sqrt{63}$

2. $\frac{1}{\sqrt{7}}$

3. $\sqrt{700}$

4. $\sqrt{7000}$

5. $\sqrt{0.07}$

6. $\sqrt{0.7}$

## 解き方の手順

1. $\sqrt{63}$:

$\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}$

$\sqrt{7} = 2.646$ なので、$\sqrt{63} = 3 \times 2.646 = 7.938$

2. $\frac{1}{\sqrt{7}}$:

$\frac{1}{\sqrt{7}} = \frac{\sqrt{7}}{7}$

$\sqrt{7} = 2.646$ なので、$\frac{1}{\sqrt{7}} = \frac{2.646}{7} = 0.378$

3. $\sqrt{700}$:

$\sqrt{700} = \sqrt{100 \times 7} = \sqrt{100} \times \sqrt{7} = 10\sqrt{7}$

$\sqrt{7} = 2.646$ なので、$\sqrt{700} = 10 \times 2.646 = 26.46$

4. $\sqrt{7000}$:

$\sqrt{7000} = \sqrt{100 \times 70} = \sqrt{100} \times \sqrt{70} = 10\sqrt{70}$

$\sqrt{70} = 8.367$ なので、$\sqrt{7000} = 10 \times 8.367 = 83.67$

5. $\sqrt{0.07}$:

$\sqrt{0.07} = \sqrt{\frac{7}{100}} = \frac{\sqrt{7}}{\sqrt{100}} = \frac{\sqrt{7}}{10}$

$\sqrt{7} = 2.646$ なので、$\sqrt{0.07} = \frac{2.646}{10} = 0.2646$

6. $\sqrt{0.7}$:

$\sqrt{0.7} = \sqrt{\frac{70}{100}} = \frac{\sqrt{70}}{\sqrt{100}} = \frac{\sqrt{70}}{10}$

$\sqrt{70} = 8.367$ なので、$\sqrt{0.7} = \frac{8.367}{10} = 0.8367$

## 最終的な答え

1. $\sqrt{63} = 7.938$

2. $\frac{1}{\sqrt{7}} = 0.378$

3. $\sqrt{700} = 26.46$

4. $\sqrt{7000} = 83.67$

5. $\sqrt{0.07} = 0.2646$

6. $\sqrt{0.7} = 0.8367$