Given sqrt{5}=2.2361 and sqrt{3}=1.7321,then | vedclass

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Question

(C) To solve $\frac{1}{\sqrt{5}-\sqrt{3}}$,we rationalize the denominator by multiplying the numerator and the denominator by the conjugate $(\sqrt{5}

Vedclass · Accepted Answer

$1.9841$

Vedclass · Answer

(C) To solve $\frac{1}{\sqrt{5}-\sqrt{3}}$,we rationalize the denominator by multiplying the numerator and the denominator by the conjugate $(\sqrt{5}+\sqrt{3})$.$\frac{1}{\sqrt{5}-\sqrt{3}} = \frac{1}{(\sqrt{5}-\sqrt{3})} 	imes \frac{(\sqrt{5}+\sqrt{3})}{(\sqrt{5}+\sqrt{3})}$Using the identity $(a-b)(a+b) = a^2 - b^2$ in the denominator:$= \frac{\sqrt{5}+\sqrt{3}}{(\sqrt{5})^2 - (\sqrt{3})^2}$$= \frac{\sqrt{5}+\sqrt{3}}{5-3} = \frac{\sqrt{5}+\sqrt{3}}{2}$Substitute the given values $\sqrt{5} = 2.2361$ and $\sqrt{3} = 1.7321$:$= \frac{2.2361 + 1.7321}{2} = \frac{3.9682}{2} = 1.9841$

Given $\sqrt{5}=2.2361$ and $\sqrt{3}=1.7321$,then $\frac{1}{\sqrt{5}-\sqrt{3}} = $

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