Question

State true or false for each of the following statements and justify in each case :

Prove that √2 is an irrational number.

Let x and y be two distinct prime numbers and p = x²y³, q = xy⁴, r = x⁵y². Find the HCF and LCM of p, q and r. Further check if HCF (p, q, r) × LCM (p, q, r) = p × q × r or not.

n² – 1 is divisible by 8, if n is

Assertion (A): Every positive even integer is a multiple of 2. Reason (R): The Fundamental Theorem of Arithmetic ensures the unique prime factorization of integers greater than 1.