Question

rationalise the denominator of the following 2+√3/2-√3​

Answer 1

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \: \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

$\frac{ {(2 + \sqrt{3}) }^{2} }{ {2}^{2} - { (\sqrt{3} )}^{2} }$

$\frac{4 + 3 + 4 \sqrt{3} }{4 - 3}$

$\frac{7 + 4 \sqrt{3} }{1} \\ 7 + 4 \sqrt{3}$

Answer 2

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Rationalise the denominator of the following 2+√3/2-√3.

$\huge\underline\mathbb{\red S\pink{O}\purple{LU} \blue{T} \orange{IO}\green{N :}}$

$\sf\:⟹\frac{ 2 + \sqrt{3}}{ 2 - \sqrt{3}}$

• Multiply both numerator & denominator with 2 + √3 .

$\sf\:⟹\frac{ 2 + \sqrt{3}}{ 2 - \sqrt{3}} × \frac{ 2 + \sqrt{3}}{ 2 + \sqrt{3}}$

$\sf\:⟹ \frac{(2 + \sqrt{3}) ( 2 + \sqrt{3})}{ (2 - \sqrt{3})(2 + \sqrt{3})}$

$\sf\:⟹ \frac{(2 + \sqrt{3})^{2}}{(2 - \sqrt{3})(2 + \sqrt{3}) }$

• (a + b)² = a² + b² + 2ab
• (a + b)(a - b) = a² - b²

$\sf\:⟹ \frac{(2)^{2} + (\sqrt{3})^{2} + 2(2)(\sqrt{3})}{(2) ^{2} - (\sqrt{3})^{2}}$

$\sf\:⟹ \frac{4 + 3 + 4\sqrt{3}}{4 - 3}$

$\sf\:⟹ 7 + 4\sqrt{3}$

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