Question

√20+√11/√20-√11 simplify

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{20} + \sqrt{11} }{ \sqrt{20} - \sqrt{11} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{ \sqrt{20} + \sqrt{11} }{ \sqrt{20} - \sqrt{11} } \times \frac{ \sqrt{20} + \sqrt{11} }{ \sqrt{20} + \sqrt{11} } \\ \\ using \: the \: identities \\ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{ {( \sqrt{20}) }^{2} + {( \sqrt{11} )}^{2} + 2 \times \sqrt{20} \times \sqrt{11} }{ {( \sqrt{20} )}^{2} - {( \sqrt{11} })^{2} } \\ \\ = \frac{20 + 11 + 2 \sqrt{220} }{20 - 11} \\ \\ = \frac{31 + 2 \sqrt{2 \times 2 \times 5 \times 11} }{9} \\ \\ = \frac{3 + 2 \times 2 \sqrt{55} }{9} \\ \\ = \frac{3 + 4 \sqrt{55} }{9}$

Hope this helps!!!!

@Mahak24

Thanks...
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