Question

помогите пожалуйста дам 100 баллов​

Answer 1

Ответ:

1)

$2$

2)

$\frac{43}{40}$

3)

$2$

4)

$9 - 2 \sqrt{8}$

5)

$6.07$

6)

$- 6 \sqrt{2}$

7)

$2$

8)

$36$

Пошаговое объяснение:

1)

$\frac{24}{(2 \sqrt{3}) {}^{2} } = \frac{24}{4 \times 3} = \frac{24}{12} = 2$

2)

$\sqrt{ \frac{9}{64} } + \sqrt{ \frac{49}{100} } = \frac{ \sqrt{9} }{ \sqrt{64} } + \\ + \frac{ \sqrt{49} }{ \sqrt{100} } = \\ = \frac{3}{8} + \frac{7}{10} = \\ = \frac{3 \times 10 + 7 \times 8}{8 \times 10} = \\ = \frac{30 + 56}{80} = \frac{86}{80} = \\ = \frac{2 \times 43}{2 \times 40} = \frac{43}{40}$

3)

$( \sqrt{7} - \sqrt{5} )( \sqrt{7} + \sqrt{5} ) = \\ = ( \sqrt{7} ) {}^{2} - ( \sqrt{5} ) {}^{2} = \\ = 7 - 5 = 2$

4)

$( \sqrt{8} - 1) {}^{2} = ( \sqrt{8} ) {}^{2} - 2 \times \\ \times 1 \times \sqrt{8} + 1{}^{2} = \\ = 8 - 2 \sqrt{8} + 1 = \\ = 9 - 2 \sqrt{} 8$

5)

$0.7 \sqrt{0.01} + \frac{2}{3} \sqrt{81} = \\ = 0.7 \times 0.1 + \frac{2}{3} \times 9 = \\ = 0.7 \times 0.1 + 2 \times 3 = \\ = 0.07 + 6 = 6.07$

6)

$2 \sqrt{50} - 5 \sqrt{2} - 3 \sqrt{32} = \\ = 2 \times \sqrt{2 \times 25} - 5 \sqrt{2} - 3 \sqrt{2 \times 16} = \\ = 2 \times \sqrt{2} \times \sqrt{25} - 5 \sqrt{2} - 3 \times \sqrt{2} \times \sqrt{16} = \\ = 2 \times 5 \times \sqrt{2} - 5 \sqrt{2} - 3 \times 4 \times \sqrt{2} = \\ = 10 \sqrt{2} - 5 \sqrt{2} - 12 \sqrt{} 2 = \\ = - 6 \sqrt{2}$

7)

$\frac{ \sqrt{12} }{ \sqrt{3} } = \sqrt{ \frac{12}{3} } = \sqrt{4} = 2$

8)

$\sqrt{22 {}^{0} \times 6 {}^{4} } = \sqrt{1 \times 6 {}^{4} } = \\ = \sqrt{6 {}^{4} } = 6 {}^{ \frac{4}{2} } = 6 {}^{2} = 36$