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Mathematics

The number (23)2(2 - \sqrt{3})^2 is

  1. a natural number
  2. an integer
  3. a rational number
  4. an irrational number

Rational Irrational Nos

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Answer

(23)2(2 - \sqrt{3})^2 = (2)2+(3)22×2×3(2)^2 + (\sqrt{3})^2 - 2 × 2 × \sqrt{3} = 4 + 3 - 434\sqrt{3} = 7 - 434\sqrt{3}

Since, 7 - 434\sqrt{3} is an irrational number therefore, (23)2(2 - \sqrt{3})^2 is also an irrational number.

∴ Option 4, is the correct option.

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