Question

Rationalise the denominator and simplify.
1)√3-√2/√3+√2​

Answer 1

Answer:

$★7+52★ \\ </p><p></p><p>Step-by-step explanation: \\ </p><p></p><p>:\implies\:\sf \dfrac{1 + \sqrt{2}}{3 - 2 \sqrt{2}} \\ </p><p></p><p>\begin{gathered}\\\\\end{gathered} \\ </p><p></p><p>:\implies\:\sf \dfrac{1 + \sqrt{2}}{3 - 2 \sqrt{2}} \: \times \: \sf \dfrac{3 + 2 \sqrt{2}}{3 - 2 \sqrt{2}} \\ </p><p></p><p>\begin{gathered}\\\\\end{gathered} \\ </p><p></p><p>:\implies\:\sf \dfrac{3 + 2\sqrt{2} \: + \: 3 \sqrt{2} \: + \: 2 \sqrt{4} }{(3)^{2} - (2\sqrt{2})^{2} }\\ </p><p></p><p>\begin{gathered}\\\\\end{gathered} \\ </p><p></p><p>:\implies\:\sf \dfrac{3 + 5\sqrt{2} \: + \: 2 \: \times \: \sqrt{2 \: \times \: 2} }{9 \: - \: 4\: \times \: 2 } \\ </p><p></p><p>\begin{gathered}\\\\\end{gathered} \\ </p><p></p><p>:\implies\:\sf \dfrac{3 \: + \: 5\sqrt{2} \: + \: 2 \: \times \: 2 }{9 \: - \: 4 \: \times \: 2 }: \\ </p><p></p><p>\begin{gathered}\\\\\end{gathered} \\ </p><p></p><p>:\implies\:\sf \dfrac{3 \: + \: 5\sqrt{2} \: + \: 4 }{9 \: - \: 8} \\ </p><p></p><p>\begin{gathered}\\\\\end{gathered} \\ </p><p></p><p>:\implies\:\sf \dfrac{3 \: + \: 5\sqrt{2} \: + \: 4 }{1} \\ </p><p></p><p>\begin{gathered}\\\\\end{gathered} \\ </p><p></p><p>: \implies {\underline{\boxed{\sf \: \: 7 + 5 \sqrt{2}}} } \: \: \: \bigg \lgroup \: \bf{Required \: Answer} \: \bigg \rgroup \\ </p><p></p><p>$

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