Question

88 89 и 90 пжжжжжжжжж

Answer 1

88)

$\sqrt{81 \times 16} = \sqrt{ {9}^{2} \times {4}^{2} } = 9 \times 4 = 36$

$\sqrt{0.09 \times 2} = \sqrt{ {0.3}^{2} \times {5}^{2} } = 0.3 \times 5 = 1.5$

$\sqrt{0.01 \times 0.04 \times 121} = \sqrt{0.1 {}^{2} \times {0.2}^{2} \times {11}^{2} } = \\ 0.1 \times 0.2 \times 11 = 0.22$

$\sqrt{30 \frac{1}{4} \times \frac{49}{36} } = \sqrt{ \frac{ {11}^{2} \times {7}^{2} }{ {2}^{2} \times {6}^{2} } } = \\ \frac{11 \times 7}{2 \times 6} = \frac{77}{12 } = 6 \frac{5}{12}$

$\sqrt{ {6}^{4} \times {4}^{2} } = \sqrt{ ({6}^{2} {)}^{2} \times {4}^{2} } = \\ 6 {}^{2} \times 4 = 36 \times 4 = 144$

$\sqrt{( - 2) {}^{6} \times 0.3 {}^{4} \times ( - 4) {}^{2} } = \\ \sqrt{ (( - 2) {}^{3}) {}^{2} \times (0.3 {}^{2} ) {}^{2} \times ( - 4) {}^{2} } = \\ 2{}^{3} \times 0.3 {}^{2} \times 4 = 8 \times 0.09 \times 4 = \\ 2.88$

89)

$\sqrt{72} \times \sqrt{2} = \sqrt{ {6}^{2} \times 2 \times 2 } = 6 \times 2 = 12$

$\sqrt{360} \times \sqrt{490} = \sqrt{ {6}^{2} \times {7}^{2} \times 10 \times 10} = \\ 6 \times 7 \times 10 = 42 \times 10 = 420$

$\frac{ \sqrt{242} }{ \sqrt{2} } = \sqrt{121} = \sqrt{ {11}^{2} } = 11$

$\frac{ \sqrt{40} }{ \sqrt{0.025} } = \sqrt{ \frac{40000}{25} } = \sqrt{ \frac{ {200}^{2} }{ {5}^{2} } } = \frac{200}{5} = 40$

90)

$\sqrt{75 \times 27} = \sqrt{ {5}^{2} \times 3 \times 3 \times {3}^{2} } = \\ 5 \times 3 \times 3 = 5 \times 9 = 45$

$\sqrt{72 \times 200} = \sqrt{ {6}^{2} \times 2 \times 2 \times {10}^{2} } = \\ 6 \times 2 \times 10 = 12 \times 10 = 120$

$\sqrt{1.6 \times 14.4} = \sqrt{ \frac{16 \times 144}{100} } = \sqrt{ \frac{ {4}^{2} \times {12}^{2} }{ {10}^{2} } } = \\ \frac{4 \times 12}{10} = \frac{48}{10} = 4.8$

$\sqrt{1690 \times 6.4} = \sqrt{169 \times 64} = \sqrt{ {13}^{2} \times {8}^{2} } = \\ 13 \times 8 = 104$