KnowledgeBoat Logo
|

Mathematics

Assertion (A): The rationalising factor of 2 + 3\sqrt{3} is 2 - 3\sqrt{3}.

Reason (R): Both 2 + 3\sqrt{3} and 2 - 3\sqrt{3} are surds.

  1. Assertion (A) is true, Reason (R) is false.

  2. Assertion (A) is false, Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Rational Numbers

2 Likes

Answer

Multiplying 2 + 3\sqrt{3} and 2 - 3\sqrt{3}

⇒(2+3)(2−3)⇒2(2−3)+3(2−3)⇒4−23+23−(3)2⇒4−3⇒1.\Rightarrow (2 + \sqrt{3})(2 - \sqrt{3}) \\[1em] \Rightarrow 2(2 - \sqrt{3}) + \sqrt{3}(2 - \sqrt{3}) \\[1em] \Rightarrow 4 - 2\sqrt{3} + 2\sqrt{3} - (\sqrt{3})^2 \\[1em] \Rightarrow 4 - 3 \\[1em] \Rightarrow 1.

Since, 1 is a rational number.

Thus, we can say that the rationalising factor of 2 + 3\sqrt{3} is 2 - 3\sqrt{3}.

∴ Assertion (A) is true.

A surd is an irrational root of a rational number.

Thus, 2 + 3\sqrt{3} and 2 - 3\sqrt{3} are irrational numbers containing surds (3)(\sqrt{3}), but not surd itself.

∴ Reason (R) is false.

Hence, option 1 is the correct option.

Answered By

2 Likes

Related Questions