frac{1}{sqrt{9}-sqrt{8}} is equal to | vedclass

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Question

(B) Given expression: $\frac{1}{\sqrt{9}-\sqrt{8}}$Since $\sqrt{9} = 3$ and $\sqrt{8} = \sqrt{4 	imes 2} = 2\sqrt{2}$,the expression becomes:$\frac{1

Vedclass · Accepted Answer

$3+2 \sqrt{2}$

Vedclass · Answer

(B) Given expression: $\frac{1}{\sqrt{9}-\sqrt{8}}$Since $\sqrt{9} = 3$ and $\sqrt{8} = \sqrt{4 	imes 2} = 2\sqrt{2}$,the expression becomes:$\frac{1}{3-2\sqrt{2}}$To rationalize the denominator,multiply the numerator and denominator by the conjugate $(3+2\sqrt{2})$:$\frac{1}{3-2\sqrt{2}} 	imes \frac{3+2\sqrt{2}}{3+2\sqrt{2}} = \frac{3+2\sqrt{2}}{(3)^2 - (2\sqrt{2})^2}$Simplify the denominator:$(3)^2 - (2\sqrt{2})^2 = 9 - (4 	imes 2) = 9 - 8 = 1$Thus,the expression simplifies to:$\frac{3+2\sqrt{2}}{1} = 3+2\sqrt{2}$Hence,option $(B)$ is the correct answer.

$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

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