Question

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Answer 1

Объяснение:

Задание 1.152

$\sqrt{ \frac{12}{25} \sqrt{ \frac{244}{15( {38}^{2} - {23}^{2}) } } } = \sqrt{ \frac{12}{25} \sqrt{ \frac{244}{15(38 - 23)(38 + 23)} } } = \sqrt{ \frac{12}{25} \sqrt{ \frac{244}{ {15}^{2} \times 61 } } } = \sqrt{ \frac{12}{25} \sqrt{ \frac{4}{ {15}^{2} } } } = \sqrt{ \frac{12}{25} \times \frac{2}{15} } = \sqrt{ \frac{4 \times 2}{25 \times 5} } = \sqrt{ \frac{8}{125} } =$

$\sqrt[3]{ \frac{8}{125} } = \frac{2}{5}$

Задание 1.154

$\sqrt[3]{29 + \sqrt{( {27}^{2} - {22}^{2}) - 5 } } = \sqrt[3]{29 + \sqrt{5 \times 49 - 5} } = \sqrt[3]{29 + \sqrt{240} } = \sqrt[3]{29 + 4 \sqrt{15} }$

Задание 1.156

$\sqrt[3]{ \frac{23}{64} + \sqrt{ \frac{5}{ {48}^{2} - {32}^{2} } } } = \sqrt[3]{ \frac{23}{64} + \sqrt{ \frac{5}{16 \times 80} } } = \sqrt[3]{ \frac{23}{64} + \sqrt{ \frac{1}{ {16}^{2} } } } = \sqrt[3]{ \frac{23}{64} + \frac{1}{16} } = \sqrt[3]{ \frac{27}{64} } = \frac{3}{4}$

Задание 1.158

$\sqrt[3]{ \frac{400 \sqrt{ {23}^{2} - {17}^{2} } }{ \sqrt{0.6} } } = \sqrt[3]{ \frac{400 \sqrt{6 \times 40} }{ \sqrt{0.6} } } = \sqrt[3]{ \frac{400 \sqrt{6 \times 40 \times 0.6} }{0.6} } = \sqrt[3]{ \frac{400 \sqrt{144} }{0.6} } = \sqrt[3]{ \frac{400 \times 12}{0.6} } = \sqrt[3]{400 \times 20} = \sqrt[3]{ {20}^{3} } = 20$

Задание 1.160

$\sqrt{58 + \sqrt{ \frac{ {44}^{2} - {26}^{2} }{35} } } = \sqrt{58 + \sqrt{ \frac{18 \times 70}{35} } } = \sqrt{58 + \sqrt{36} } = \sqrt{58 + 6} = \sqrt{64} = 8$