a,b are positive integers. If 21ab2 and 15ab are perfect squares, the minimum value of a + b is
1.If p is a factor of a perfect square, then p2 must also be a factor, where p is a prime.
21ab2 = 3.7.ab2
b2 is a perfect square. So the smallest value of a is 3 x 7,
∴ a = 3 x 7 = 21
15 ab = 3.5.a.b
∴ The smallest value of b is 5 x 7 = 35.
∴ a + b = 21 + 35= 56