Question

$\sqrt[6]{25 + 4 \sqrt{6} } - \sqrt[3]{1 + 2 \sqrt{6 } }$
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Answer 1

Ответ:

= 0

Объяснение:

1.

$\sqrt[6]{25 + 4\sqrt{6}} =\sqrt[6]{25 + 2 \times 2 \sqrt{6}}=$

$= \sqrt[6]{25 + 2 \times 2\sqrt{6} + {(2\sqrt{6}}^{2}) - {(2 \sqrt{6}}^{2}} =$

$= \sqrt[6]{1 + 2 \times 2 \sqrt{6} + {(2 \sqrt{6}}^{2})} = \sqrt[6]{ {(1 + 2 \sqrt{6})}^{2}} =$

$= {(1 + 2 \sqrt{6})}^{ \frac{2}{6}} = {(1 + 2 \sqrt{6})}^{ \frac{1}{3}} =$

$= \sqrt[3]{1 + 2 \sqrt{6}}$

2.

$\sqrt[3]{1 + 2 \sqrt{6}} - \sqrt[3]{1 + 2 \sqrt{6}} = 0$