Question

Let p, q and r be three distinct prime numbers. Check whether p · q · r + q is a composite number or not. Further, give an example for 3 distinct primes p, q, r such that

Prove that √3 is an irrational number.

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.