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

\frac{\sqrt{7} + 2}{3}

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\frac{\sqrt{7} - 2}{3}

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\frac{\sqrt{7} + 2}{5}

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\frac{\sqrt{7} + 2}{45}

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Solution

The correct option is C $\frac{\sqrt{7} + 2}{3}$
We use the identity $(a + \sqrt{b}) (a - \sqrt{b}) = a^{2} - b$ .
Multiply and divide $\frac{1}{\sqrt{7} - 2}$ by $\sqrt{7} + 2$ to get
$\frac{1}{\sqrt{7} - 2} \times \frac{\sqrt{7} + 2}{\sqrt{7} + 2} = \frac{\sqrt{7} + 2}{7 - 4} = \frac{\sqrt{7} + 2}{3}$

Hence, option $A .$

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Similar questions

Question 12
The number obtained on rationalising the denominator of $\frac{1}{\sqrt{7} - 2}$ is

A) $\frac{\sqrt{7} + 2}{3}$
B) $\frac{\sqrt{7} - 2}{3}$
C) $\frac{\sqrt{7} + 2}{5}$
D) $\frac{\sqrt{7} + 2}{45}$

Q. Question 12
The number obtained on rationalising the denominator of

\frac{1}{\sqrt{7} - 2}

is

A)

\frac{\sqrt{7} + 2}{3}

\frac{\sqrt{7} - 2}{3}

\frac{\sqrt{7} + 2}{5}

\frac{\sqrt{7} + 2}{45}

Q. Simplify each of the following by rationalizing the denominator:
i)

\frac{6 - 4 \sqrt{2}}{6 + 4 \sqrt{2}}

ii)

\frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} + \sqrt{5}}

iii)

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

Q. Simplify the following by rationalizing the denominator.

\frac{3 \sqrt{5} - \sqrt{7}}{2 \sqrt{3} + \sqrt{2}}

Q. Rationalize the denominator:

\frac{1}{2 \sqrt{7} + 3 \sqrt{3}}

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The number obtained on rationalizing the denominator of 1√7−2 is

The correct option is C √7+23We use the identity (a+√b)(a−√b)=a2−b.Multiply and divide 1√7−2 by √7+2 to get 1√7−2×√7+2√7+2=√7+27−4=√7+23 Hence, option A.

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