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Mathematics

27\sqrt{27} is irrational and 3\sqrt{3} is also irrational, then which of the following is rational:

  1. 273\sqrt{27} - \sqrt{3}

  2. 27+3\sqrt{27} + \sqrt{3}

  3. 27×3\sqrt{27} \times \sqrt{3}

  4. none of these

Rational Irrational Nos

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Answer

As we know that

27×3=81=9.\Rightarrow \sqrt{27} \times \sqrt{3}\\[1em] = \sqrt{81}\\[1em] = 9.

9 is rational number. So, 27×3\sqrt{27} \times \sqrt{3} is also a rational number.

Hence, option 3 is the correct option.

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