√72 1) √2 4) √(-5)2; 7) √56.40.√35; 10) √56; 13) √10.72.√10.26; 72 16) (2√3)2 19) (√19-√2)(√19+√2); 27) √(36a^4)/(b^2 )при а = 6 и b = 9; √51.√12 22) √17 25) 4√17 5√2-√34; 1 28) - √10-3 1 √10+3 31) (4√2-7)2+4√2; 34) (√45-√5) √5; √4a11.√9b4 18) при а = 7 √a7b4 и в = 9; 21) √49х2у при х = 5 и у = 3; 24) √a4 -(-а)2 при а = 3; 1 30) -х^4у^6 при х = 3 4 и у = 2; 32) √a² + 12ab + 36b2 при 2 3 a = 7иb=; 5 36) √a26ab +962 при а = 3 и b = 6.

1) \[\frac{\sqrt{72}}{\sqrt{2}}\]

• \[\frac{\sqrt{72}}{\sqrt{2}} = \sqrt{\frac{72}{2}} = \sqrt{36} = 6\]

Ответ: 6

4) \[\sqrt{(-5)^2}\]

• \[\sqrt{(-5)^2} = |-5| = 5\]

Ответ: 5

7) \[\sqrt{56 \cdot 40} \cdot \sqrt{35}\]

• \[\sqrt{56 \cdot 40} \cdot \sqrt{35} = \sqrt{56 \cdot 40 \cdot 35} = \sqrt{8 \cdot 7 \cdot 8 \cdot 5 \cdot 7 \cdot 5} = \sqrt{8^2 \cdot 7^2 \cdot 5^2} = 8 \cdot 7 \cdot 5 = 280\]

Ответ: 280

10) \[\sqrt{56}\]

• \[\sqrt{56} = \sqrt{4 \cdot 14} = 2\sqrt{14}\]

Ответ: \[2\sqrt{14}\]

13) \[\sqrt{10} \cdot 7^2 \cdot \sqrt{10} \cdot 26\]

• \[\sqrt{10} \cdot 7^2 \cdot \sqrt{10} \cdot 26 = 7^2 \cdot 26 \cdot \sqrt{10} \cdot \sqrt{10} = 49 \cdot 26 \cdot 10 = 12740\]

Ответ: 12740

16) \[\frac{72}{(2\sqrt{3})^2}\]

• \[\frac{72}{(2\sqrt{3})^2} = \frac{72}{4 \cdot 3} = \frac{72}{12} = 6\]

Ответ: 6

19) \[(\sqrt{19} - \sqrt{2})(\sqrt{19} + \sqrt{2})\]

• \[(\sqrt{19} - \sqrt{2})(\sqrt{19} + \sqrt{2}) = (\sqrt{19})^2 - (\sqrt{2})^2 = 19 - 2 = 17\]

Ответ: 17

22) \[\frac{\sqrt{51} \cdot \sqrt{12}}{\sqrt{17}}\]

• \[\frac{\sqrt{51} \cdot \sqrt{12}}{\sqrt{17}} = \frac{\sqrt{3 \cdot 17} \cdot \sqrt{4 \cdot 3}}{\sqrt{17}} = \frac{\sqrt{3} \cdot \sqrt{17} \cdot 2 \cdot \sqrt{3}}{\sqrt{17}} = 2 \cdot 3 = 6\]

Ответ: 6

25) \[4\sqrt{17} \cdot 5\sqrt{2} - \sqrt{34}\]

• \[4\sqrt{17} \cdot 5\sqrt{2} - \sqrt{34} = 20\sqrt{17} \cdot \sqrt{2} - \sqrt{17 \cdot 2} = 20\sqrt{34} - \sqrt{34} = 19\sqrt{34}\]

Ответ: \[19\sqrt{34}\]

28) \[\frac{1}{\sqrt{10} - 3} - \frac{1}{\sqrt{10} + 3}\]

• \[\frac{1}{\sqrt{10} - 3} - \frac{1}{\sqrt{10} + 3} = \frac{(\sqrt{10} + 3) - (\sqrt{10} - 3)}{(\sqrt{10} - 3)(\sqrt{10} + 3)} = \frac{\sqrt{10} + 3 - \sqrt{10} + 3}{10 - 9} = \frac{6}{1} = 6\]

Ответ: 6

31) \[(4\sqrt{2} - 7)^2 + 4\sqrt{2}\]

• \[(4\sqrt{2} - 7)^2 + 4\sqrt{2} = (4\sqrt{2})^2 - 2 \cdot 4\sqrt{2} \cdot 7 + 7^2 + 4\sqrt{2} = 16 \cdot 2 - 56\sqrt{2} + 49 + 4\sqrt{2} = 32 - 52\sqrt{2} + 49 = 81 - 52\sqrt{2}\]

Ответ: \[81 - 52\sqrt{2}\]

34) \[(\sqrt{45} - \sqrt{5}) \cdot \sqrt{5}\]

• \[(\sqrt{45} - \sqrt{5}) \cdot \sqrt{5} = \sqrt{45} \cdot \sqrt{5} - \sqrt{5} \cdot \sqrt{5} = \sqrt{9 \cdot 5} \cdot \sqrt{5} - 5 = 3\sqrt{5} \cdot \sqrt{5} - 5 = 3 \cdot 5 - 5 = 15 - 5 = 10\]

Ответ: 10

18) \[\frac{\sqrt{4a^{11}} \cdot \sqrt{9b^4}}{\sqrt{a^7b^4}}\] при a = 7 и b = 9

• \[\frac{\sqrt{4a^{11}} \cdot \sqrt{9b^4}}{\sqrt{a^7b^4}} = \frac{\sqrt{4} \cdot \sqrt{a^{11}} \cdot \sqrt{9} \cdot \sqrt{b^4}}{\sqrt{a^7} \cdot \sqrt{b^4}} = \frac{2 \cdot a^{11/2} \cdot 3 \cdot b^2}{a^{7/2} \cdot b^2} = \frac{6 \cdot a^{11/2}}{a^{7/2}} = 6 \cdot a^{(11/2 - 7/2)} = 6 \cdot a^{4/2} = 6 \cdot a^2\]
• Подставляем значения a и b:
• \[6 \cdot 7^2 = 6 \cdot 49 = 294\]

Ответ: 294

21) \[\sqrt{49x^2y^4}\] при x = 5 и y = 3

• \[\sqrt{49x^2y^4} = \sqrt{49} \cdot \sqrt{x^2} \cdot \sqrt{y^4} = 7 \cdot |x| \cdot y^2\]
• Подставляем значения x и y:
• \[7 \cdot |5| \cdot 3^2 = 7 \cdot 5 \cdot 9 = 315\]

Ответ: 315

24) \[\sqrt{a^4 - (-a)^2}\] при a = 3

• \[\sqrt{a^4 - (-a)^2} = \sqrt{a^4 - a^2} = \sqrt{a^2(a^2 - 1)} = |a| \cdot \sqrt{a^2 - 1}\]
• Подставляем значение a:
• \[|3| \cdot \sqrt{3^2 - 1} = 3 \cdot \sqrt{9 - 1} = 3\sqrt{8} = 3\sqrt{4 \cdot 2} = 3 \cdot 2\sqrt{2} = 6\sqrt{2}\]

Ответ: \[6\sqrt{2}\]

27) \[\sqrt{\frac{36a^4}{b^2}}\] при a = 6 и b = 9

• \[\sqrt{\frac{36a^4}{b^2}} = \frac{\sqrt{36a^4}}{\sqrt{b^2}} = \frac{\sqrt{36} \cdot \sqrt{a^4}}{|b|} = \frac{6 \cdot a^2}{|b|}\]
• Подставляем значения a и b:
• \[\frac{6 \cdot 6^2}{|9|} = \frac{6 \cdot 36}{9} = \frac{216}{9} = 24\]

Ответ: 24

30) \[- \frac{1}{4}x^4y^6\] при x = 3 и y = 2

• \[-\frac{1}{4}x^4y^6 = -\frac{1}{4} \cdot 3^4 \cdot 2^6 = -\frac{1}{4} \cdot 81 \cdot 64 = -81 \cdot 16 = -1296\]

Ответ: -1296

32) \[\sqrt{a^2 + 12ab + 36b^2}\] при a = \[7\frac{2}{5}\] и b = \frac{3}{5}

• \[\sqrt{a^2 + 12ab + 36b^2} = \sqrt{(a + 6b)^2} = |a + 6b|\]
• Подставляем значения a и b:
• \[|7\frac{2}{5} + 6 \cdot \frac{3}{5}| = |\frac{37}{5} + \frac{18}{5}| = |\frac{55}{5}| = |11| = 11\]

Ответ: 11

36) \[\sqrt{a^2 - 6ab + 9b^2}\] при a = 3 и b = 6

• \[\sqrt{a^2 - 6ab + 9b^2} = \sqrt{(a - 3b)^2} = |a - 3b|\]
• Подставляем значения a и b:
• \[|3 - 3 \cdot 6| = |3 - 18| = |-15| = 15\]

Ответ: 15