与えられた平方根の数を $a\sqrt{b}$ の形に変形する問題です。

1. 問題の内容

与えられた平方根の数を $a\sqrt{b}$ の形に変形する問題です。

2. 解き方の手順

各問題について、平方根の中の数を素因数分解し、平方数を取り出すことで、$a\sqrt{b}$ の形に変形します。

(5) $\sqrt{28}$

$28 = 4 \times 7 = 2^2 \times 7$

$\sqrt{28} = \sqrt{2^2 \times 7} = \sqrt{2^2} \times \sqrt{7} = 2\sqrt{7}$

(6) $\sqrt{20}$

$20 = 4 \times 5 = 2^2 \times 5$

$\sqrt{20} = \sqrt{2^2 \times 5} = \sqrt{2^2} \times \sqrt{5} = 2\sqrt{5}$

(7) $\sqrt{72}$

$72 = 36 \times 2 = 6^2 \times 2$

$\sqrt{72} = \sqrt{6^2 \times 2} = \sqrt{6^2} \times \sqrt{2} = 6\sqrt{2}$

(8) $\sqrt{90}$

$90 = 9 \times 10 = 3^2 \times 10$

$\sqrt{90} = \sqrt{3^2 \times 10} = \sqrt{3^2} \times \sqrt{10} = 3\sqrt{10}$

(9) $\sqrt{125}$

$125 = 25 \times 5 = 5^2 \times 5$

$\sqrt{125} = \sqrt{5^2 \times 5} = \sqrt{5^2} \times \sqrt{5} = 5\sqrt{5}$

(10) $\sqrt{112}$

$112 = 16 \times 7 = 4^2 \times 7$

$\sqrt{112} = \sqrt{4^2 \times 7} = \sqrt{4^2} \times \sqrt{7} = 4\sqrt{7}$

(11) $\sqrt{50}$

$50 = 25 \times 2 = 5^2 \times 2$

$\sqrt{50} = \sqrt{5^2 \times 2} = \sqrt{5^2} \times \sqrt{2} = 5\sqrt{2}$

(12) $\sqrt{63}$

$63 = 9 \times 7 = 3^2 \times 7$

$\sqrt{63} = \sqrt{3^2 \times 7} = \sqrt{3^2} \times \sqrt{7} = 3\sqrt{7}$

(13) $\sqrt{44}$

$44 = 4 \times 11 = 2^2 \times 11$

$\sqrt{44} = \sqrt{2^2 \times 11} = \sqrt{2^2} \times \sqrt{11} = 2\sqrt{11}$

(14) $\sqrt{500}$

$500 = 100 \times 5 = 10^2 \times 5$

$\sqrt{500} = \sqrt{10^2 \times 5} = \sqrt{10^2} \times \sqrt{5} = 10\sqrt{5}$

(15) $\sqrt{48}$

$48 = 16 \times 3 = 4^2 \times 3$

$\sqrt{48} = \sqrt{4^2 \times 3} = \sqrt{4^2} \times \sqrt{3} = 4\sqrt{3}$

(16) $\sqrt{96}$

$96 = 16 \times 6 = 4^2 \times 6$

$\sqrt{96} = \sqrt{4^2 \times 6} = \sqrt{4^2} \times \sqrt{6} = 4\sqrt{6}$

(1) $\sqrt{8}$

$8 = 4 \times 2 = 2^2 \times 2$

$\sqrt{8} = \sqrt{2^2 \times 2} = \sqrt{2^2} \times \sqrt{2} = 2\sqrt{2}$

(2) $\sqrt{12}$

$12 = 4 \times 3 = 2^2 \times 3$

$\sqrt{12} = \sqrt{2^2 \times 3} = \sqrt{2^2} \times \sqrt{3} = 2\sqrt{3}$

(3) $\sqrt{24}$

$24 = 4 \times 6 = 2^2 \times 6$

$\sqrt{24} = \sqrt{2^2 \times 6} = \sqrt{2^2} \times \sqrt{6} = 2\sqrt{6}$

(4) $\sqrt{18}$

$18 = 9 \times 2 = 3^2 \times 2$

$\sqrt{18} = \sqrt{3^2 \times 2} = \sqrt{3^2} \times \sqrt{2} = 3\sqrt{2}$

3. 最終的な答え

(1) $2\sqrt{2}$

(2) $2\sqrt{3}$

(3) $2\sqrt{6}$

(4) $3\sqrt{2}$

(5) $2\sqrt{7}$

(6) $2\sqrt{5}$

(7) $6\sqrt{2}$

(8) $3\sqrt{10}$

(9) $5\sqrt{5}$

(10) $4\sqrt{7}$

(11) $5\sqrt{2}$

(12) $3\sqrt{7}$

(13) $2\sqrt{11}$

(14) $10\sqrt{5}$

(15) $4\sqrt{3}$

(16) $4\sqrt{6}$