Question

rationalise the denominator of each of the following 1/2√5-√3​

Answer 1

$\large {\pmb{\mathfrak{\purple{Question:-}}}}$

Rationalise the denominator of the following :

$\sf \dfrac{1}{2 \sqrt{5} - \sqrt{3} }$

$\large {\pmb{\mathfrak{\purple{Solution:-}}}}$

$~~\sf \leadsto \dfrac{1}{2\sqrt{5}-\sqrt{3}}$

$\: \: \: \sf \leadsto \dfrac{1}{2 \sqrt{5} - \sqrt{3} } \times ( \dfrac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } )$

Using the identity :

$\sf (a+b)(a-b)=a^2-b^2$

$\: \: \sf \leadsto \dfrac{2 \sqrt{5} + \sqrt{3} }{ {(2 \sqrt{5} )}^{2} - {( \sqrt{3}) }^{2} }$

$\: \: \sf \leadsto \dfrac{2 \sqrt{5} + \sqrt{3} }{(4 \times 5) - 3}$

$\: \: \sf \leadsto \dfrac{2 \sqrt{5} + \sqrt{3} }{20 - 3}$

$\: \: \sf \leadsto \dfrac{2 \sqrt{5} + \sqrt{3} }{17}$

$\large {\pmb{\mathfrak{\purple{Know~more:-}}}}$

• $\sf (a+b)^2=a^2+b^2+2ab$

• $\sf (a-b)^2=a^2+b^2-2ab$

• $\sf (a+b)^3=a^2+b^3+3ab(a+b)$

• $\sf (a-b)^3=a^2-b^2-3ab(a-b)$

• $\sf a^3+b^3=(a+b)(a^2+b^2-ab)$