Number Systems · Class 9 · CBSE Mathematics

Rationalize the denominator of frac{1}{sqrt{7} - 2}.

Practice question from Number Systems (Class 9 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-BBDAC7

Rationalize the denominator of 17−2\frac{1}{\sqrt{7} - 2}.

  1. A.\frac{\sqrt{7} + 2}{3}Correct answer
  2. B.\frac{\sqrt{7} - 2}{3}
  3. C.\sqrt{7} + 2
  4. D.\frac{\sqrt{7} + 2}{5}

Solution

To rationalize the denominator, multiply the numerator and the denominator by the conjugate 7+2\sqrt{7} + 2. This gives 1(7+2)(7−2)(7+2)=7+2(7)2−22=7+27−4=7+23\frac{1(\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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