与えられた式を計算し、簡単にします。

はい、承知いたしました。画像にある問題のうち、以下の問題を解きます。

* (2) $\sqrt{63} \div \sqrt{2}$

* (3) $\sqrt{12} \div \sqrt{21}$

* (5) $(-14\sqrt{2}) \div \sqrt{28}$

* (6) $(-9\sqrt{3}) \div (-15\sqrt{7})$

* (8) $\sqrt{143} \div \sqrt{39}$

* (9) $\sqrt{75} \div \sqrt{30}$

以下、それぞれの問題について、問題の内容、解き方の手順、最終的な答えを記述します。

1. 問題の内容

与えられた式を計算し、簡単にします。

2. 解き方の手順

(2) $\sqrt{63} \div \sqrt{2}$

$\sqrt{63} \div \sqrt{2} = \frac{\sqrt{63}}{\sqrt{2}} = \sqrt{\frac{63}{2}} = \sqrt{\frac{63 \times 2}{2 \times 2}} = \sqrt{\frac{126}{4}} = \frac{\sqrt{126}}{2} = \frac{\sqrt{9 \times 14}}{2} = \frac{3\sqrt{14}}{2}$

(3) $\sqrt{12} \div \sqrt{21}$

$\sqrt{12} \div \sqrt{21} = \frac{\sqrt{12}}{\sqrt{21}} = \sqrt{\frac{12}{21}} = \sqrt{\frac{4}{7}} = \frac{\sqrt{4}}{\sqrt{7}} = \frac{2}{\sqrt{7}} = \frac{2\sqrt{7}}{7}$

(5) $(-14\sqrt{2}) \div \sqrt{28}$

$(-14\sqrt{2}) \div \sqrt{28} = \frac{-14\sqrt{2}}{\sqrt{28}} = \frac{-14\sqrt{2}}{\sqrt{4 \times 7}} = \frac{-14\sqrt{2}}{2\sqrt{7}} = \frac{-7\sqrt{2}}{\sqrt{7}} = \frac{-7\sqrt{2} \times \sqrt{7}}{\sqrt{7} \times \sqrt{7}} = \frac{-7\sqrt{14}}{7} = -\sqrt{14}$

(6) $(-9\sqrt{3}) \div (-15\sqrt{7})$

$(-9\sqrt{3}) \div (-15\sqrt{7}) = \frac{-9\sqrt{3}}{-15\sqrt{7}} = \frac{9\sqrt{3}}{15\sqrt{7}} = \frac{3\sqrt{3}}{5\sqrt{7}} = \frac{3\sqrt{3} \times \sqrt{7}}{5\sqrt{7} \times \sqrt{7}} = \frac{3\sqrt{21}}{35}$

(8) $\sqrt{143} \div \sqrt{39}$

$\sqrt{143} \div \sqrt{39} = \frac{\sqrt{143}}{\sqrt{39}} = \sqrt{\frac{143}{39}} = \sqrt{\frac{11 \times 13}{3 \times 13}} = \sqrt{\frac{11}{3}} = \frac{\sqrt{11}}{\sqrt{3}} = \frac{\sqrt{11} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{\sqrt{33}}{3}$

(9) $\sqrt{75} \div \sqrt{30}$

$\sqrt{75} \div \sqrt{30} = \frac{\sqrt{75}}{\sqrt{30}} = \sqrt{\frac{75}{30}} = \sqrt{\frac{5 \times 15}{2 \times 15}} = \sqrt{\frac{5}{2}} = \frac{\sqrt{5}}{\sqrt{2}} = \frac{\sqrt{5} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{\sqrt{10}}{2}$

3. 最終的な答え

(2) $\frac{3\sqrt{14}}{2}$

(3) $\frac{2\sqrt{7}}{7}$

(5) $-\sqrt{14}$

(6) $\frac{3\sqrt{21}}{35}$

(8) $\frac{\sqrt{33}}{3}$

(9) $\frac{\sqrt{10}}{2}$