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Which one is correct

A. 3\sqrt{3} is irrational

B. Sum of two irrational number is always irrational

C. p\sqrt{p}, where pp is prime, is irrational

D. Every composite number can be expressed as a product of primes

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 1

3\sqrt{3} is irrational, and p\sqrt{p} is irrational for every prime pp. By the Fundamental Theorem of Arithmetic every composite number factorises into primes. Statement B fails: (2+2)+(2−2)=4(2 + \sqrt{2}) + (2 - \sqrt{2}) = 4, a rational sum of two irrationals. Hence A, C and D only.

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