Question

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

Answer 1

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