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Explanation:

500 = 22 × 53

For (a + b)(a+b) to be divisible by 500, it should have power of 2 as well as 5 in it.

∴ a + b should have power of both 2 as well as 5.

The least such number is 1010.

∴ a + b = 10.

∴ a × b is minimum when a = 9 and b = 1 (or vice-versa)

Hence, the least possible value is 9.

Hence, option (b).

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