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 :

If x = ab³ and y = a³b, where a and b are prime numbers, then [HCF (x, y) – LCM (x, y)] is equal to :

Prove that √2 is an irrational number.