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Mathematics

Which of the following is an irrational number

  1. 49\sqrt{\dfrac{4}{9}}

  2. 123\dfrac{\sqrt{12}}{\sqrt{3}}

  3. 7\sqrt{7}

  4. 81\sqrt{81}

Rational Irrational Nos

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Answer

49\sqrt{\dfrac{4}{9}} = 49\dfrac{\sqrt{4}}{\sqrt{9}} = (2)2(3)2\dfrac{(\sqrt{2})^2}{(\sqrt{3})^2} = 23\dfrac{2}{3} is a rational number .

123\dfrac{\sqrt{12}}{\sqrt{3}} = 2×2×33\dfrac{\sqrt{2 × 2 × 3}}{\sqrt{3}} = 233\dfrac{2\sqrt{3}}{\sqrt{3}} = 2 is a rational number.

7\sqrt{7} is an irrational number.

81\sqrt{81} = 9×9\sqrt{9 × 9} = 9 is a rational number.

∴ Option 3, is the correct option.

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