IBPS Clerk Prelims Model Paper 10

Question : 10 of 100

Marks: +1, -0

\frac{1}{\sqrt{9}-\sqrt{8}}

= ?

Solution:

Concept:

Rationalize the denominator by multiplying with its conjugate.

Explanation:

Simplify:

\sqrt{9}=3

and

\sqrt{8}=2\sqrt{2}

So the expression becomes

\frac{1}{3-2\sqrt{2}}

Multiply numerator and denominator by the conjugate

3+2\sqrt{2}

\frac{1}{3-2\sqrt{2}} \times \frac{3+2\sqrt{2}}{3+2\sqrt{2}} = \frac{3+2\sqrt{2}}{(3)^2-(2\sqrt{2})^2}

Now,

(3)^2=9

and

(2\sqrt{2})^2=8

So denominator

=9-8=1

Thus, the expression simplifies to

3+2\sqrt{2}

Answer:

3+2\sqrt{2}

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