Question

simplify: (√32-√5) ^1/3 (√32-√5) ^1/3​

Answer 1

$: \implies\underline{\boxed{\sf { \sqrt[3]{37 - 8 \sqrt{10} } }}}$

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$\begin{gathered}:\implies\sf (4 \sqrt{2 } - \sqrt{5} {)}^{ \frac{1}{3} } \times ( \sqrt{32} - \sqrt{5} {)}^{ \frac{1}{3} } \\\\\\:\implies\sf (4 \sqrt{2 } - \sqrt{5} {)}^{ \frac{1}{3} } \times ( \sqrt[4]{2} - \sqrt{5} {)}^{ \frac{1}{3}}\\\\\\:\implies\sf (4 \sqrt{2} - \sqrt{5} {)}^{ \frac{2}{3} } \\\\\\:\implies\sf \sqrt[3]{(4 \sqrt{2} - \sqrt{5} {)}^{2} } \\\\\\:\implies\sf \sqrt[3]{32 - 8 \sqrt{10} + 5 } \\\\\\:\implies\underline{\boxed{\sf { \sqrt[3]{37 - 8 \sqrt{10} } }}}\end{gathered} ⠀$

$\underline { \sf \:\:\therefore{ \sqrt[3]{37 - 8 \sqrt{10} } }}$

Answer 2

Answer:

please thank my all question