Question

Квадратные корни, нужно полное решение!

Answer 1

А8)
$sqrt{ frac{12 times 50 times 2}{147} } = sqrt{ frac{12 times 25 times 2 times 2}{49 times3 } } = sqrt { frac{4 times 25 times 4}{49}} = frac{2 times 2 times 5}{7} = frac{20}{7}$
Ответ: 3)

Б1)
${ sqrt{7 - 2 sqrt{6} } - sqrt{7 + 2 sqrt{6} }) }^{2} = 7 - 2 sqrt{6} - 2 sqrt{7 - 2 sqrt{6} } sqrt{7 + 2 sqrt{6} } + 7 + 2 sqrt{6} = 14 - 2 sqrt{ {7}^{2} - {(2 sqrt{6}) }^{2} } = 14 - 2 sqrt{49 - 24} = 14 - 2 sqrt{25} = 14 - 2 times 5 = 14 - 10 = 4$
Б2)
$frac{1}{3 sqrt{7} - 7} - frac{1}{7 + 3 sqrt{7} } = frac{3 sqrt{7} + 7 - (3 sqrt{7} - 7) }{(3 sqrt{7} - 7)(3 sqrt{7} + 7) } = frac{3 sqrt{7} + 7 - 3 sqrt{7} + 7}{ {(3 sqrt{7}) }^{2} - {7}^{2} } = frac{14}{63 - 49} = frac{14}{14} = 1$