Задание 36. Сравните значения выражений: 1) 2√2>√7,2√2 = √8, √8>√7. 2) 3√6... √60 3) 2√5... √21 4) 3√4... 6 5) √40... 2/11 6) 4/2... √30 7) 4√5... √80 8) 2√7...5 9) 6√3... 10 10) 3√3... √10 11) 2√3...3√2 12) 5√2...3√5 13) -2√5...-3√2 14) 5√3...6√2 15) 3/10...7√2 16) -10/5...-5/10 17) -2√8...-4√2 18) -2√1,1... -3/1,5 19) 10/20... 20/10 20) -0,2√5... -0,5√2 Задание 37. Расположите числа в порядке возрастания 1) 3√5, 2√7, 4√2 2) 5√2, 2√11, √51 3) -6, -2√10, -√39 4) -2√6, -3√3, -5 5) 10,6√3,7√2 Расположите числа в порядке убывания 6) √60, 8, 3√7 7) -2√3,-3,- √11 8) 2√15, 10, 3/10 9)-2/10,-1,-10√6 10) √17, 3√2, 2√5

36. 1) 2√2 >√7, 2√2 = √8, √8 > √7. (Уже дано) 2) 3√6 ... √60 $$(3\sqrt{6})^2 = 9 \cdot 6 = 54$$ $$(\sqrt{60})^2 = 60$$ $$54 < 60$$ 3√6 < √60 3) 2√5 ... √21 $$(2\sqrt{5})^2 = 4 \cdot 5 = 20$$ $$(\sqrt{21})^2 = 21$$ $$20 < 21$$ 2√5 < √21 4) 3√4 ... 6 $$3\sqrt{4} = 3 \cdot 2 = 6$$ 3√4 = 6 5) √40 ... 2√11 $$(\sqrt{40})^2 = 40$$ $$(2\sqrt{11})^2 = 4 \cdot 11 = 44$$ $$40 < 44$$ √40 < 2√11 6) 4√2 ... √30 $$(4\sqrt{2})^2 = 16 \cdot 2 = 32$$ $$(\sqrt{30})^2 = 30$$ $$32 > 30$$ 4√2 > √30 7) 4√5 ... √80 $$(4\sqrt{5})^2 = 16 \cdot 5 = 80$$ $$(\sqrt{80})^2 = 80$$ $$80 = 80$$ 4√5 = √80 8) 2√7 ... 5 $$(2\sqrt{7})^2 = 4 \cdot 7 = 28$$ $$5^2 = 25$$ $$28 > 25$$ 2√7 > 5 9) 6√3 ... 10 $$(6\sqrt{3})^2 = 36 \cdot 3 = 108$$ $$10^2 = 100$$ $$108 > 100$$ 6√3 > 10 10) 3√3 ... √10 $$(3\sqrt{3})^2 = 9 \cdot 3 = 27$$ $$(\sqrt{10})^2 = 10$$ $$27 > 10$$ 3√3 > √10 11) 2√3 ... 3√2 $$(2\sqrt{3})^2 = 4 \cdot 3 = 12$$ $$(3\sqrt{2})^2 = 9 \cdot 2 = 18$$ $$12 < 18$$ 2√3 < 3√2 12) 5√2 ... 3√5 $$(5\sqrt{2})^2 = 25 \cdot 2 = 50$$ $$(3\sqrt{5})^2 = 9 \cdot 5 = 45$$ $$50 > 45$$ 5√2 > 3√5 13) -2√5 ... -3√2 $$-2\sqrt{5} = -\sqrt{4 \cdot 5} = -\sqrt{20}$$ $$-3\sqrt{2} = -\sqrt{9 \cdot 2} = -\sqrt{18}$$ $$- \sqrt{20} < -\sqrt{18}$$ -2√5 < -3√2 14) 5√3 ... 6√2 $$(5\sqrt{3})^2 = 25 \cdot 3 = 75$$ $$(6\sqrt{2})^2 = 36 \cdot 2 = 72$$ $$75 > 72$$ 5√3 > 6√2 15) 3√10 ... 7√2 $$(3\sqrt{10})^2 = 9 \cdot 10 = 90$$ $$(7\sqrt{2})^2 = 49 \cdot 2 = 98$$ $$90 < 98$$ 3√10 < 7√2 16) -10√5 ... -5√10 $$-10\sqrt{5} = -\sqrt{100 \cdot 5} = -\sqrt{500}$$ $$-5\sqrt{10} = -\sqrt{25 \cdot 10} = -\sqrt{250}$$ $$- \sqrt{500} < -\sqrt{250}$$ -10√5 < -5√10 17) -2√8 ... -4√2 $$-2\sqrt{8} = -\sqrt{4 \cdot 8} = -\sqrt{32}$$ $$-4\sqrt{2} = -\sqrt{16 \cdot 2} = -\sqrt{32}$$ $$- \sqrt{32} = -\sqrt{32}$$ -2√8 = -4√2 18) -2√1,1 ... -3√1,5 $$-2\sqrt{1,1} = -\sqrt{4 \cdot 1,1} = -\sqrt{4,4}$$ $$-3\sqrt{1,5} = -\sqrt{9 \cdot 1,5} = -\sqrt{13,5}$$ $$- \sqrt{4,4} > -\sqrt{13,5}$$ -2√1,1 > -3√1,5 19) 10√20 ... 20√10 $$(10\sqrt{20})^2 = 100 \cdot 20 = 2000$$ $$(20\sqrt{10})^2 = 400 \cdot 10 = 4000$$ $$2000 < 4000$$ 10√20 < 20√10 20) -0,2√5 ... -0,5√2 $$-0,2\sqrt{5} = -\sqrt{0,04 \cdot 5} = -\sqrt{0,2}$$ $$-0,5\sqrt{2} = -\sqrt{0,25 \cdot 2} = -\sqrt{0,5}$$ $$- \sqrt{0,2} > -\sqrt{0,5}$$ -0,2√5 > -0,5√2 Задание 37. Расположите числа в порядке возрастания 1) 3√5, 2√7, 4√2 $$3\sqrt{5} = \sqrt{9 \cdot 5} = \sqrt{45}$$ $$2\sqrt{7} = \sqrt{4 \cdot 7} = \sqrt{28}$$ $$4\sqrt{2} = \sqrt{16 \cdot 2} = \sqrt{32}$$ $$\sqrt{28} < \sqrt{32} < \sqrt{45}$$ 2√7, 4√2, 3√5 2) 5√2, 2√11, √51 $$5\sqrt{2} = \sqrt{25 \cdot 2} = \sqrt{50}$$ $$2\sqrt{11} = \sqrt{4 \cdot 11} = \sqrt{44}$$ $$\sqrt{44} < \sqrt{50} < \sqrt{51}$$ 2√11, 5√2, √51 3) -6, -2√10, -√39 $$-6 = -\sqrt{36}$$ $$-2\sqrt{10} = -\sqrt{4 \cdot 10} = -\sqrt{40}$$ $$-6 > -\sqrt{39} > -2\sqrt{10}$$ -6, -√39, -2√10 4) -2√6, -3√3, -5 $$-2\sqrt{6} = -\sqrt{4 \cdot 6} = -\sqrt{24}$$ $$-3\sqrt{3} = -\sqrt{9 \cdot 3} = -\sqrt{27}$$ $$-5 = -\sqrt{25}$$ $$-2\sqrt{6} > -5 > -3\sqrt{3}$$ -2√6, -5, -3√3 5) 10, 6√3, 7√2 $$6\sqrt{3} = \sqrt{36 \cdot 3} = \sqrt{108}$$ $$7\sqrt{2} = \sqrt{49 \cdot 2} = \sqrt{98}$$ $$7\sqrt{2} < 10 < 6\sqrt{3}$$ 7√2, 10, 6√3 Расположите числа в порядке убывания 6) √60, 8, 3√7 $$3\sqrt{7} = \sqrt{9 \cdot 7} = \sqrt{63}$$ $$8 = \sqrt{64}$$ √60 < 3√7 < 8 8, 3√7, √60 7) -2√3, -3, -√11 $$-2\sqrt{3} = -\sqrt{4 \cdot 3} = -\sqrt{12}$$ $$-3 = -\sqrt{9}$$ $$-3 > -\sqrt{11} > -2\sqrt{3}$$ -3, -√11, -2√3 8) 2√15, 10, 3√10 $$2\sqrt{15} = \sqrt{4 \cdot 15} = \sqrt{60}$$ $$3\sqrt{10} = \sqrt{9 \cdot 10} = \sqrt{90}$$ $$2\sqrt{15} < 3\sqrt{10} < 10$$ 10, 3√10, 2√15 9) -2√10, -1, -10√6 $$-2\sqrt{10} = -\sqrt{4 \cdot 10} = -\sqrt{40}$$ $$-1 = -\sqrt{1}$$ $$-10\sqrt{6} = -\sqrt{100 \cdot 6} = -\sqrt{600}$$ $$-1 > -2\sqrt{10} > -10\sqrt{6}$$ -1, -2√10, -10√6 10) √17, 3√2, 2√5 $$3\sqrt{2} = \sqrt{9 \cdot 2} = \sqrt{18}$$ $$2\sqrt{5} = \sqrt{4 \cdot 5} = \sqrt{20}$$ $$\sqrt{17} < 3\sqrt{2} < 2\sqrt{5}$$ 2√5, 3√2, √17