Question

Упростите выражения:

Answer 1

$\sqrt{50} - 2 \sqrt[3]{3} - \sqrt{32} + \sqrt[3]{81} + 2 \sqrt{2} = \sqrt{2 \times 25} - 2 \sqrt[3]{3} - \sqrt{2 \times 16} + \sqrt[3]{27 \times 3} + 2 \sqrt{2} = 5\sqrt{2} - 2 \sqrt[3]{3} - 4 \sqrt{2} + 3 \sqrt[3]{3} + 2 \sqrt{2} = (5 \sqrt{2} - 4 \sqrt{2} + 2 \sqrt{2} ) + (3 \sqrt[3]{3} - 2 \sqrt[3]{3} ) = 3 \sqrt{2} + \sqrt[3]{3}$

$\frac{1}{2} \times ( \frac{1}{ \sqrt[8]{m} + \sqrt[8]{n}} - \frac{1}{ \sqrt[8]{m} - \sqrt[8]{n} } ) \times ( \sqrt[4]{n} - \sqrt[4]{m} ) = \frac{1}{2} \times ( \frac{( \sqrt[8]{m} - \sqrt[8]{n} ) - ( \sqrt[8]{m} + \sqrt[8]{n} )}{( \sqrt[8]{m} + \sqrt[8]{n} )( \sqrt[8]{m} - \sqrt[8]{n} )} ) \times ( \sqrt[4]{n} - \sqrt[4]{m} ) = \frac{1}{2} \times \frac{ - 2 \sqrt[8]{n} }{ {( \sqrt[8]{m} )}^{2} - {( \sqrt[8]{n} )}^{2} } \times ( \sqrt[4]{n} - \sqrt[4]{m} ) = \frac{ - 2 \sqrt[8]{n} \times ( \sqrt[4]{n} - \sqrt[4]{m} )}{2 \times ( \sqrt[4]{m} - \sqrt[4]{n}) } = \frac{ \sqrt[8]{n} ( \sqrt[4]{m} - \sqrt[4]{n} )}{ \sqrt[4]{m} - \sqrt[4]{n} } = \sqrt[8]{n}$