Question

5/(√3+√2) Rationalise the denominator​

Answer 1

To Rationalize :-

• $\sf \dfrac{5}{\sqrt{3} +\sqrt{2} }$

Identity Used :-

• $\sf{(a+b)(a-b)={\underline{\green{\underline{\pmb{a^{2}-b^{2}}}}}}}$

Solution :-

• In order to rationalize the denominator, we have to multiply the number with the denominator's inverse.Multiplying by  
• $\sf\dfrac{\sqrt{3} -\sqrt{2} }{\sqrt{3} -\sqrt{2} }$

$\sf \red{\: \: \: \: \: \: :\implies \dfrac{5}{\sqrt{3} +\sqrt{2} }}$

$\: \: \: \: \: \: \::\implies \sf \dfrac{5}{\sqrt{3} +\sqrt{2} } \times \dfrac{\sqrt{3}-\sqrt{2} }{\sqrt{3}-\sqrt{2}}$

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

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

$\: \: \: \: \: \: \::\implies \sf \dfrac{5\sqrt{3} - 5\sqrt{2} }{(3 ) - (2 ) }$

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

$\: \: \: \: \: \: \:\red{:\implies \sf = 5\sqrt{3} - 5\sqrt{2}}$

More Identities :-

• $\sf{(a+b)(a+b)={\green{\underline{\underline{\pmb{a^{2}+2ab+b^{2}}}}}}}$

• $\sf{(a-b)(a-b)={\green{\underline{\underline{\pmb{a^{2}-2ab+b^{2}}}}}}}$

• $\sf{(a+b)(a-b)={\underline{\green{\underline{\pmb{a^{2}-b^{2}}}}}}}$

• $\sf{(x+a)(x+b)={\green{\underline{\underline{\pmb{x^{2}+(a+b)x+ab}}}}}}$

• $\sf{(a-b)² ={\green{\underline{\underline{\pmb{a² - 2ab + b²}}}}}}$

• $\sf{ (a+b+c)²={\green{\underline{\underline{\pmb{a² + b² + c² + 2ab + 2bc + 2ca}}}}}}$