Question

91.Найдите значение выражения
$1)\sqrt{72} *\sqrt{2}. 2) \sqrt{360} *\sqrt{490} 3) \frac{\sqrt{242}}{\sqrt{2}} 1)\sqrt{25a}+\sqrt{36a} -\sqrt{49a } 2)\sqrt{27} -\sqrt{12} +\sqrt{300} 3)3\sqrt{32a} -5\sqrt{98a}+\frac{1}{3} \sqrt{288a}$

Answer 1

$1) \: \: \sqrt{72} \times \sqrt{2} = \sqrt{72 \times 2} = \sqrt{144} = 12 \\ \\ 2) \: \sqrt{360} \times \sqrt{490} = \sqrt{360 \times 490} = \sqrt{36 \times 10 \times 49 \times 10} = \sqrt{36 \times 49 \times 100} = 6 \times 7 \times 10 = 420 \\ \\ 3) \: \frac{ \sqrt{242} }{ \sqrt{2} } = \sqrt{ \frac{242}{2} } = \sqrt{121} = 11 \\ \\ 1) \: \sqrt{25a} + \sqrt{36a} - \sqrt{49a} = \sqrt{25} \times \sqrt{a} + \sqrt{36} \times \sqrt{a} - \sqrt{49} \times \sqrt{a} = 5a + 6a - 7a = 4a \\ \\ 2) \: \sqrt{27} - \sqrt{12} + \sqrt{300} = \sqrt{9 \times 3} - \sqrt{4 \times 3} + \sqrt{100 \times 3} = \sqrt{9} \times \sqrt{3} - \sqrt{4} \times \sqrt{3} + \sqrt{100} \times \sqrt{3} = 3 \sqrt{3} - 2 \sqrt{3} + 10 \sqrt{3} = 11 \sqrt{3} \\ \\ 3) \: 3 \sqrt{32a} - 5 \sqrt{98a} + \frac{1}{3} \sqrt{288a} = 3 \sqrt{16 \times 2a} - 5 \sqrt{49 \times 2a} + \frac{1}{3} \sqrt{144 \times 2a} = 3 \sqrt{ 1 6} \times \sqrt{2a} - 5 \sqrt{49} \times \sqrt{2a} + \frac{1}{3} \sqrt{144} \times \sqrt{2a} = 3 \times 4 \times \sqrt{2a} - 5 \times 7 \times \sqrt{2a} + \frac{1}{3} \times 12 \sqrt{2a} = 12 \sqrt{2a} - 35 \sqrt{2a} + 4 \sqrt{2a} = - 19 \sqrt{2a}$