Question

(√32-√5)^1\3×(√32+√5)^1\3

Answer 1

Answer

3 is the answer

Answer 2

$\red { ( \sqrt{32} - \sqrt{5} )^{\frac{1}{3}} \times ( \sqrt{32} + \sqrt{5} )^{\frac{1}{3}} }$

$= \Big(( \sqrt{32} - \sqrt{5} )( \sqrt{32} + \sqrt{5} )\Big)^{\frac{1}{3}}$

$\blue { We\:are \:using \: following \: formulae :}$

$\pink {i)a^{m} \times b^{m} = (ab)^{m} }$

$\pink {ii) (a^{m})^{n} = a^{m \times n }}\\\pink { iii) (a + b )(a - b) = a^{2} - b^{2} }$

$= [ (\sqrt{32})^{2} - (\sqrt{5})^{2})^{\frac{1}{3}}$

$= ( 32 - 5 )^{\frac{1}{3}} \\= 27^{\frac{1}{3}}\\= (3^{3})^{\frac{1}{3}} \\= (3)^{3 \times \frac{1}{3}} \\= 3$

Therefore.,

$\red { ( \sqrt{32} - \sqrt{5} )^{\frac{1}{3}} \times ( \sqrt{32} + \sqrt{5} )^{\frac{1}{3}} }\green {= 3}$

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