The number obtained by rationalising the denominator of $\frac{1}{\sqrt{7} + 2}$ is .

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Solution

Given: $\frac{1}{\sqrt{7} + 2}$

Rationalising the denominator,

$= \frac{(\sqrt{7} - 2)}{(\sqrt{7} + 2) (\sqrt{7} - 2)}$

$= \frac{\sqrt{7} - 2}{(\sqrt{7})^{2} - (2)^{2}}$

$= \frac{\sqrt{7} - 2}{7 - 4}$

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

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Q. The number obtained on rationalising the denominator of

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

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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}

Simplify $\frac{1}{2 - \sqrt{7}}$ by rationalising the denominator.

Q. find the number obtained on rationalising the denominator of 2/root11 - 3

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Number Theory: Interesting Results

Standard X Mathematics

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The number obtained by rationalising the denominator of 1√7+2 is .

Given: 1√7+2 Rationalising the denominator, =(√7−2)(√7+2)(√7−2) =√7−2(√7)2−(2)2 =√7−27−4 =√7−23

The number obtained by rationalising the denominator of $\frac{1}{\sqrt{7} + 2}$ is .

Given: $\frac{1}{\sqrt{7} + 2}$

Rationalising the denominator,

$= \frac{(\sqrt{7} - 2)}{(\sqrt{7} + 2) (\sqrt{7} - 2)}$

$= \frac{\sqrt{7} - 2}{(\sqrt{7})^{2} - (2)^{2}}$

$= \frac{\sqrt{7} - 2}{7 - 4}$

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