Question

Assertion (A):√a is an irrational number,where a is a prime number.
Reason(R):Square root of any prime number is an irrational number.​

Answer 1

$\huge \underline{\bf{Answer :- }}$

Assertion (A): :- That is, let p be a prime number then prove that p is irrational. ... But first, let's define a prime number. A prime number is a positive integer greater than 1 that has exactly two positive integer divisors: namely, 1 and itself.

Reason(R): :- Sal proves that the square root of any prime number must be an irrational number. For example, because of this proof we can quickly determine that √3, √5, √7, or √11 are irrational numbers.

Answer 2

Assertion (A) √a is an irrational number, where a is a prime number that is true, but Reason (R) Square root of any prime number is an irrational number. is not a correct explanation for it.

As per the question given,

Assertion (A) is true, but Reason (R) is not a correct explanation for it.

Assertion (A) states that the square root of a prime number is an irrational number, which is true. For example, the square root of 2, 3, 5, 7, 11, etc. are all irrational numbers.

Reason (R) states that the square root of any prime number is an irrational number, which is also true. However, this is not a complete explanation for Assertion (A). There are other types of numbers besides prime numbers that also have irrational square roots, such as non-square integers and composite numbers.

Therefore, Assertion (A) is true, but Reason (R) is not a correct explanation for it.

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