画像に写っている数学の問題のうち、以下の問題を解きます。 (1) $\sqrt{5} \times \sqrt{6}$ (2) $\sqrt{10} \times (-\sqrt{7})$ (3) $\sqrt{12} \times \sqrt{3}$ (4) $\frac{\sqrt{12}}{\sqrt{2}}$ (5) $\frac{\sqrt{88}}{\sqrt{8}}$ (6) $(-\sqrt{54}) \div (-\sqrt{6})$ (7) $2\sqrt{6}$ (8) $6\sqrt{5}$ (9) $4\sqrt{3}$ (10) $\frac{\sqrt{7}}{3}$ (11) $\sqrt{\frac{3}{4}}$ (12) $\sqrt{\frac{10}{5}}$ (13) $\sqrt{45}$ (14) $\sqrt{160}$ (15) $\sqrt{500}$ (16) $\sqrt{56}$ (17) $\sqrt{162}$ (18) $\sqrt{252}$ (19) $\sqrt{\frac{5}{81}}$ (20) $\sqrt{0.06}$ (21) $\sqrt{0.0027}$ (22) $(-\sqrt{12}) \times (-\sqrt{5})$ (23) $\sqrt{18} \times \sqrt{27}$ (24) $\sqrt{45} \times \sqrt{8}$ (25) $\sqrt{14} \times \sqrt{35}$ (26) $\sqrt{15} \times \sqrt{30}$ (27) $\sqrt{26} \times (-\sqrt{39})$ (28) $\sqrt{12} \times \sqrt{96}$ (29) $\sqrt{18} \times (-\sqrt{32})$ (30) $\sqrt{24} \times \sqrt{54}$

1. 問題の内容

画像に写っている数学の問題のうち、以下の問題を解きます。

(1) $\sqrt{5} \times \sqrt{6}$

(2) $\sqrt{10} \times (-\sqrt{7})$

(3) $\sqrt{12} \times \sqrt{3}$

(4) $\frac{\sqrt{12}}{\sqrt{2}}$

(5) $\frac{\sqrt{88}}{\sqrt{8}}$

(6) $(-\sqrt{54}) \div (-\sqrt{6})$

(7) $2\sqrt{6}$

(8) $6\sqrt{5}$

(9) $4\sqrt{3}$

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

(11) $\sqrt{\frac{3}{4}}$

(12) $\sqrt{\frac{10}{5}}$

(13) $\sqrt{45}$

(14) $\sqrt{160}$

(15) $\sqrt{500}$

(16) $\sqrt{56}$

(17) $\sqrt{162}$

(18) $\sqrt{252}$

(19) $\sqrt{\frac{5}{81}}$

(20) $\sqrt{0.06}$

(21) $\sqrt{0.0027}$

(22) $(-\sqrt{12}) \times (-\sqrt{5})$

(23) $\sqrt{18} \times \sqrt{27}$

(24) $\sqrt{45} \times \sqrt{8}$

(25) $\sqrt{14} \times \sqrt{35}$

(26) $\sqrt{15} \times \sqrt{30}$

(27) $\sqrt{26} \times (-\sqrt{39})$

(28) $\sqrt{12} \times \sqrt{96}$

(29) $\sqrt{18} \times (-\sqrt{32})$

(30) $\sqrt{24} \times \sqrt{54}$

2. 解き方の手順

(1) $\sqrt{5} \times \sqrt{6} = \sqrt{5 \times 6} = \sqrt{30}$

(2) $\sqrt{10} \times (-\sqrt{7}) = -\sqrt{10 \times 7} = -\sqrt{70}$

(3) $\sqrt{12} \times \sqrt{3} = \sqrt{12 \times 3} = \sqrt{36} = 6$

(4) $\frac{\sqrt{12}}{\sqrt{2}} = \sqrt{\frac{12}{2}} = \sqrt{6}$

(5) $\frac{\sqrt{88}}{\sqrt{8}} = \sqrt{\frac{88}{8}} = \sqrt{11}$

(6) $(-\sqrt{54}) \div (-\sqrt{6}) = \sqrt{\frac{54}{6}} = \sqrt{9} = 3$

(7) $2\sqrt{6} = \sqrt{2^2 \times 6} = \sqrt{4 \times 6} = \sqrt{24}$

(8) $6\sqrt{5} = \sqrt{6^2 \times 5} = \sqrt{36 \times 5} = \sqrt{180}$

(9) $4\sqrt{3} = \sqrt{4^2 \times 3} = \sqrt{16 \times 3} = \sqrt{48}$

(10) これは既に $\frac{\sqrt{a}}{b}$ の形なので、そのまま。$\frac{\sqrt{7}}{3}$

(11) $\sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}} = \frac{\sqrt{3}}{2}$

(12) $\sqrt{\frac{10}{5}} = \sqrt{2}$

(13) $\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}$

(14) $\sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10}$

(15) $\sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5}$

(16) $\sqrt{56} = \sqrt{4 \times 14} = \sqrt{4} \times \sqrt{14} = 2\sqrt{14}$

(17) $\sqrt{162} = \sqrt{81 \times 2} = \sqrt{81} \times \sqrt{2} = 9\sqrt{2}$

(18) $\sqrt{252} = \sqrt{36 \times 7} = \sqrt{36} \times \sqrt{7} = 6\sqrt{7}$

(19) $\sqrt{\frac{5}{81}} = \frac{\sqrt{5}}{\sqrt{81}} = \frac{\sqrt{5}}{9}$

(20) $\sqrt{0.06} = \sqrt{\frac{6}{100}} = \frac{\sqrt{6}}{\sqrt{100}} = \frac{\sqrt{6}}{10}$

(21) $\sqrt{0.0027} = \sqrt{\frac{27}{10000}} = \frac{\sqrt{27}}{\sqrt{10000}} = \frac{\sqrt{9 \times 3}}{100} = \frac{3\sqrt{3}}{100}$

(22) $(-\sqrt{12}) \times (-\sqrt{5}) = \sqrt{12 \times 5} = \sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15}$

(23) $\sqrt{18} \times \sqrt{27} = \sqrt{18 \times 27} = \sqrt{486} = \sqrt{81 \times 6} = \sqrt{81} \times \sqrt{6} = 9\sqrt{6}$

(24) $\sqrt{45} \times \sqrt{8} = \sqrt{45 \times 8} = \sqrt{360} = \sqrt{36 \times 10} = \sqrt{36} \times \sqrt{10} = 6\sqrt{10}$

(25) $\sqrt{14} \times \sqrt{35} = \sqrt{14 \times 35} = \sqrt{490} = \sqrt{49 \times 10} = \sqrt{49} \times \sqrt{10} = 7\sqrt{10}$

(26) $\sqrt{15} \times \sqrt{30} = \sqrt{15 \times 30} = \sqrt{450} = \sqrt{225 \times 2} = \sqrt{225} \times \sqrt{2} = 15\sqrt{2}$

(27) $\sqrt{26} \times (-\sqrt{39}) = -\sqrt{26 \times 39} = -\sqrt{1014} = -\sqrt{9 \times 112 + 6} = -\sqrt{169 \times 6} = - \sqrt{13^2 \times 6} = - 13\sqrt{6}$

(28) $\sqrt{12} \times \sqrt{96} = \sqrt{12 \times 96} = \sqrt{1152} = \sqrt{576 \times 2} = \sqrt{576} \times \sqrt{2} = 24\sqrt{2}$

(29) $\sqrt{18} \times (-\sqrt{32}) = -\sqrt{18 \times 32} = -\sqrt{576} = -24$

(30) $\sqrt{24} \times \sqrt{54} = \sqrt{24 \times 54} = \sqrt{1296} = 36$

3. 最終的な答え

(1) $\sqrt{30}$

(2) $-\sqrt{70}$

(3) 6

(4) $\sqrt{6}$

(5) $\sqrt{11}$

(6) 3

(7) $\sqrt{24}$

(8) $\sqrt{180}$

(9) $\sqrt{48}$

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

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

(12) $\sqrt{2}$

(13) $3\sqrt{5}$

(14) $4\sqrt{10}$

(15) $10\sqrt{5}$

(16) $2\sqrt{14}$

(17) $9\sqrt{2}$

(18) $6\sqrt{7}$

(19) $\frac{\sqrt{5}}{9}$

(20) $\frac{\sqrt{6}}{10}$

(21) $\frac{3\sqrt{3}}{100}$

(22) $2\sqrt{15}$

(23) $9\sqrt{6}$

(24) $6\sqrt{10}$

(25) $7\sqrt{10}$

(26) $15\sqrt{2}$

(27) $-13\sqrt{6}$

(28) $24\sqrt{2}$

(29) $-24$

(30) 36