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Question

(A) To rationalize the denominator of $\frac{1}{7-\sqrt{2}}$,we multiply both the numerator and the denominator by the conjugate of the denominator,wh

Vedclass · Accepted Answer

$\frac{7+\sqrt{2}}{47}$

Vedclass · Answer

(A) To rationalize the denominator of $\frac{1}{7-\sqrt{2}}$,we multiply both the numerator and the denominator by the conjugate of the denominator,which is $(7+\sqrt{2})$.$\frac{1}{7-\sqrt{2}} = \frac{1}{7-\sqrt{2}} 	imes \frac{7+\sqrt{2}}{7+\sqrt{2}}$Using the identity $(a-b)(a+b) = a^2 - b^2$ in the denominator:$= \frac{7+\sqrt{2}}{(7)^2 - (\sqrt{2})^2}$$= \frac{7+\sqrt{2}}{49-2}$$= \frac{7+\sqrt{2}}{47}$Hence,option $A$ is the correct answer.

The number obtained on rationalizing the denominator of $\frac{1}{7-\sqrt{2}}$ is

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