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Mathematics

Statement 1: If a = 333\sqrt{3} and b = 512\dfrac{5}{\sqrt{12}}, then a x b is irrational.

Statement 2: a x b = 33×512=15×323=1523 \sqrt{3} \times \dfrac{5}{\sqrt{12}} = \dfrac{15 \times \sqrt{3}}{2\sqrt{3}} = \dfrac{15}{2}

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Rational Irrational Nos

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Answer

Given, a = 333\sqrt{3} and b = 512\dfrac{5}{\sqrt{12}}

⇒a×b=33×512=33×54×3=33×54×3=33×523=5×3323=15323=152=7.5\Rightarrow a \times b = 3 \sqrt{3} \times \dfrac{5}{\sqrt{12}}\\[1em] = 3 \sqrt{3} \times \dfrac{5}{\sqrt{4 \times 3}}\\[1em] = 3 \sqrt{3} \times \dfrac{5}{\sqrt{4} \times \sqrt{3}}\\[1em] = 3 \sqrt{3} \times \dfrac{5}{2\sqrt{3}}\\[1em] = \dfrac{5 \times 3 \sqrt{3}}{2\sqrt{3}}\\[1em] = \dfrac{15 \sqrt{3}}{2\sqrt{3}}\\[1em] = \dfrac{15}{2}\\[1em] = 7.5

7.5 is rational number. Thus, a x b is a rational number.

∴ Statement 1 is false, and statement 2 is true.

Hence, option 4 is correct option.

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