Question

$( \sqrt[2]{2} + \sqrt[3]{3} )( \sqrt[2]{2} - \sqrt[3]{3} )$

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Answer 1

Answer:

$(\sqrt[2]{2} + \sqrt[3]{3} )(\sqrt[2]{2} - \sqrt[3]{3} )$ $=2 - \sqrt[3]{9}$

Step-by-step explanation:

$(\sqrt[2]{2} + \sqrt[3]{3} )(\sqrt[2]{2} - \sqrt[3]{3} )$

$=(\sqrt[2]{2})^2 - (\sqrt[3]{3} )^2$  [using the identity $a^2 - b^2 = (a + b)(a - b)$]

$=2^{\frac{2}{2} } - 3^{\frac{2}{3} }$  [using the formula $\sqrt[n]{a^m} = a^{\frac{m}{n} }$]

$=2 - \sqrt[3]{3^2}$

$=2 - \sqrt[3]{9}$