Question

$\sqrt{40 \times \sqrt{10 - \frac{ \sqrt{20} }{ \sqrt{5} } } }$
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Answer 1

Ответ:

$\sqrt{40 \times \sqrt{10 - \frac{ \sqrt{20} }{5} } } = \sqrt{40 \sqrt{10 - \sqrt{4} } } = \sqrt{40 \sqrt{10 - 2} } = 2 \sqrt{10 \sqrt{10 - 2} } = 4 {}^{2} \sqrt{50}$

Answer 2

$\sqrt{40\times \sqrt{10-\frac{\sqrt{20} }{\sqrt{5} } } } =\sqrt{40\times \sqrt{10-\sqrt{4} } } =\sqrt{40\times \sqrt{10-2 } } =2\times \sqrt{10\times\sqrt{10-2} } =2\times \sqrt{\sqrt{10^2} \times \sqrt{10-2} } =2\times \sqrt{\sqrt{10^2\times(10-2)} } =2\times\sqrt{\sqrt{100\times8} } =2\times \sqrt{\sqrt{800} } =2\times\sqrt[4]{800} =4\sqrt[4]{50}$