tex]...

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[tex] \sqrt[3]{2 \sqrt{6}-5 } * \sqrt[6]{49+20 \sqrt{6} } [/tex]

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Verified answer

1) 49 + 20√6 = 5² + 2*5*2√6 + (2√6)² = (5+2√6)²
2) $\sqrt[6]{(5+2 \sqrt{6})^2} = \sqrt[3]{5+2 \sqrt{6}}$
3) $\sqrt[3]{2 \sqrt{6}-5} * \sqrt[3]{2 \sqrt{6}+5}= \sqrt[3]{(2 \sqrt{6})^2 - 5^{2} } = \sqrt[3]{24 - 25} = \sqrt[3]{-1} =-1$

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