Question

rationalize the denominator of 2√3/√11-√10​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\frac{2 \sqrt{3} }{ \sqrt{11} - \sqrt{10} } =2 \sqrt{33} + 2 \sqrt{30}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies \frac{2 \sqrt{3} }{ \sqrt{11} - \sqrt{10} } \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies \frac{2 \sqrt{3} }{ \sqrt{11} - \sqrt{10} } = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\\tt: \implies \frac{2 \sqrt{3} }{ \sqrt{11} - \sqrt{10} } \\ \\ \tt \circ \: Multiplying \: \: \frac{ \sqrt{11} + \sqrt{10} }{ \sqrt{11} + \sqrt{10} } \\ \\ \tt: \implies \frac{2 \sqrt{3} }{ \sqrt{11} - \sqrt{10} } \times \frac{ \sqrt{11} + \sqrt{10} }{ \sqrt{11} + \sqrt{10} } \\ \\ \tt: \implies \frac{2 \sqrt{3}( \sqrt{11} + \sqrt{10} ) }{( \sqrt{11} - \sqrt{10} )( \sqrt{11} + \sqrt{10}) } \\ \\ \tt \circ \: (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ \tt: \implies \frac{2 \sqrt{33} + 2 \sqrt{30} }{ (\sqrt{11})^{2} - (\sqrt{10})^{2} } \\ \\ \tt: \implies \frac{2 \sqrt{33} + 2 \sqrt{30} }{11 - 10 } \\ \\ \green{\tt: \implies 2 \sqrt{33} + 2\sqrt{30} } \\ \\ \green{\tt \therefore\frac{2 \sqrt{3} }{ \sqrt{11} - \sqrt{10} } =2 \sqrt{33} + 2 \sqrt{30} }$

Answer 2

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QUESTION :

rationalize the denominator of 2√3/√11-√10.

SOLUTION :

$\dfrac{2 \sqrt{3} }{ \sqrt{11} - \sqrt{10} }$

$Rationalizing \: Factor \: :- \dfrac{\sqrt{11} + \sqrt{10}}{\sqrt{11} - \sqrt{10}}$

$\dfrac{2 \sqrt{3} }{ \sqrt{11} - \sqrt{10} } \times \dfrac{ { \sqrt{11} + \sqrt{10} } }{ \sqrt{11} + \sqrt{10} }$

$=> 2 \sqrt{ 3 } × ( \sqrt{11} + \sqrt{10}$

$=> 2\sqrt{33} + 2 \sqrt{30}$