Question

Объясните как это сделать ​

Answer 1

15

$\sqrt{72} + \sqrt{8} - 8 \sqrt{2} + 2 = \\ = \sqrt{9 \times 8} + \sqrt{4 \times 2} - 8 \sqrt{2} + 2 = \\ = \sqrt{ {3}^{2} \times {2}^{2} \times 2} + \sqrt{ {2}^{2} \times 2} - 8 \sqrt{2} + 2 = \\ = 3 \times 2 \sqrt{2} + 2 \sqrt{2} - 8 \sqrt{2} + 2 = \\ = 6 \sqrt{2} + 2 \sqrt{2} - 8 \sqrt{2} + 2 = 2$

17

$( \sqrt{10} - 6)( \sqrt{10} + 6) = {( \sqrt{10}) }^{2} - {6}^{2} = 10 - 36 = - 26$

19

$\sqrt{54} - \sqrt{24} - \sqrt{6} + 12 = \\ = \sqrt{9 \times 6} - \sqrt{4 \times 6} - \sqrt{6} + 12 = \\ = 3 \sqrt{6} - 2 \sqrt{6} - \sqrt{6} + 12 = 12$

21

${( \sqrt{62} + 3)}^{2} - 6 \sqrt{62} = \\ = {( \sqrt{62} )}^{2} + 2 \times 3 \sqrt{62} + {3}^{2} - 6 \sqrt{62} = \\ = 62 + 6 \sqrt{62} + 9 - 6 \sqrt{62} = 71$

39

$( \sqrt{20} - \sqrt{5} ) \times \sqrt{5 } = \sqrt{20} \times \sqrt{5} - \sqrt{5} \times \sqrt{5} = \\ = \sqrt{100} - 5 = 10 - 5 = 5$

41

${(5 + \sqrt{2} )}^{2} + {(5 - \sqrt{2}) }^{2} = \\ = 25 + 10 \sqrt{2} + 2 + 25 - 10 \sqrt{2} + 2 = \\ = 50 + 4 = 54$

43

$\sqrt{ {(3 \sqrt{2} - 5)}^{2} } + 3 \sqrt{2} = \\ = |3 \sqrt{2} - 5| + 3 \sqrt{2} \\ \\ 3 \sqrt{2} < 5 = |3 \sqrt{2} - 5 | = 5 - 3 \sqrt{2} \\ \\ 5 - 3 \sqrt{2} + 3 \sqrt{2} = 5$