Question

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.

The factor tree of a number x is shown below : Find the values of x, y, a and b. Hence, write the product of the prime factors of the number x so obtained.