Question

By rationalizing the denominator of √2 by √5 + √3

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Answer 1

Step-by-step explanation:

rationalising factor is

$\sqrt{5} - \sqrt{3}$

please find the attachment

Answer 2

GiveN:-

By rationalizing the denominator of √2 by √5 + √3.

SolutioN:-

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

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

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

By using the identity a²- b² = (a+b)(a-b),

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

$\large\implies{\sf{\dfrac{\sqrt{10}-\sqrt{6}}{(\sqrt{5})^2-(\sqrt{3})^2}}}$

$\large\implies{\sf{\dfrac{\sqrt{10}-\sqrt{6}}{5-3}}}$

$\large\implies{\sf{\dfrac{\sqrt{10}-\sqrt{6}}{2}}}$

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

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

$\large\therefore\boxed{\bf{\sqrt{5}-\sqrt{3}}}$

The answer is √5 - √3.