Rationalise the denominator of frac{1}{2+sqrt | vedclass

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(B) To rationalise the denominator of $\frac{1}{2+\sqrt{3}}$,we multiply the numerator and the denominator by the conjugate of the denominator,which i

Vedclass · Accepted Answer

$2-\sqrt{3}$

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(B) To rationalise the denominator of $\frac{1}{2+\sqrt{3}}$,we multiply the numerator and the denominator by the conjugate of the denominator,which is $(2-\sqrt{3})$.$\frac{1}{2+\sqrt{3}} 	imes \frac{2-\sqrt{3}}{2-\sqrt{3}} = \frac{2-\sqrt{3}}{(2)^2 - (\sqrt{3})^2}$Using the identity $(a+b)(a-b) = a^2 - b^2$,we get:$= \frac{2-\sqrt{3}}{4-3} = \frac{2-\sqrt{3}}{1} = 2-\sqrt{3}$.

Rationalise the denominator of $\frac{1}{2+\sqrt{3}}$.

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