Assertion (A) claims that 2 + √3 is irrational precisely because it is the sum of a rational number (2) and an irrational number (√3). Reason (R) states this exact general property. Hence, Reason (R) correctly explains Assertion (A).

Assertion (A) claims that 2 + √3 is irrational precisely because it is the sum of a rational number (2) and an irrational number (√3). Reason (R) states this exact general property. Hence, Reason (R) correctly explains Assertion (A).

Assassin reason Association 2 plus square root 3 rational number reason the sum of a rational number ending rational number is always irrational

Answer: Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Step-by-step solution

Step 1: Evaluate the Reason (R)

We test whether Reason (R) is mathematically true. The difference of two rational numbers is always rational, so if the sum of a rational number and an irrational number were rational, the irrational number would have to be rational, which is impossible. Thus, the sum of a rational number and an irrational number is always irrational, making Reason (R) true.

Step 2: Evaluate the Assertion (A)

Here, $2$ is an integer and therefore a rational number, while $\sqrt{3}$ is a well-known irrational number. Adding the rational number $2$ to the irrational number $\sqrt{3}$ yields $2 + \sqrt{3}$ , which is irrational. Therefore, Assertion (A) is true.

Step 3: Determine the Relationship Between A and R

Assertion (A) claims that $2 + \sqrt{3}$ is irrational precisely because it is the sum of a rational number ( $2$ ) and an irrational number ( $\sqrt{3}$ ). Reason (R) states this exact general property. Hence, Reason (R) correctly explains Assertion (A).

Solve your own maths question free →