Question

rationalize the denominator 5 upon 4√3 - ∛2

Answer 1

[tex]\mathfrak{\huge{Answer:-}} \\ \bold{ \frac{5}{4 \sqrt{3} - 3 \sqrt{2} } } \\ = \frac{5}{4 \sqrt{3} - 3 \sqrt{2} } \times \frac{4 \sqrt{3} + 3 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \\ = \frac{5(4 \sqrt{3} + 3 \sqrt{2}) }{(4 \sqrt{3} - 3 \sqrt{2})(4 \sqrt{3} + 3 \sqrt{2} )} \\ = \frac{5(4 \sqrt{3} + 3 \sqrt{2})}{ {(4 \sqrt{3}) }^{2} - {(3 \sqrt{2}) }^{2}} \\ = \frac{5(4 \sqrt{3} + 3 \sqrt{2})}{48 - 18} \\ = \frac{5(4 \sqrt{3} + 3 \sqrt{2} )}{30} \\ = \frac{4 \sqrt{3} + 3 \sqrt{2} }{6} \\ \large{\boxed{\boxed{\bold{ \frac{5}{4 \sqrt{3} - 3 \sqrt{2}} = \frac{4 \sqrt{3} + 3 \sqrt{2}}{6}}}}}[/tex]