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Mathematics

The number obtained on rationalising the denominator of 172{\dfrac{1}{\sqrt{7} - 2}} is

  1. 7+23{\dfrac{\sqrt{7} + 2}{3}}

  2. 723{\dfrac{\sqrt{7} - 2}{3}}

  3. 7+25{\dfrac{\sqrt{7} + 2}{5}}

  4. 7+245{\dfrac{\sqrt{7} + 2}{45}}

Rational Irrational Nos

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Answer

Given,

172{\dfrac{1}{\sqrt{7} - 2}}

Let us rationalise the denominator,

Then,

172=172×7+27+27+2(7)2227+2747+23{\dfrac{1}{\sqrt{7} - 2}} = {\dfrac{1}{\sqrt{7} - 2}} × \dfrac{\sqrt{7} + 2}{\sqrt{7} + 2} \\[1.5em] \Rightarrow \dfrac{\sqrt{7} + 2}{(\sqrt{7})^2 - {2}^2} \\[1.5em] \Rightarrow \dfrac{\sqrt{7} + 2}{7 - 4} \\[1.5em] \Rightarrow \dfrac{\sqrt{7} + 2}{3} \\[1.5em]

∴ Option 1, is the correct option.

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