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To have a whole number square root, the number is a perfect square.

Thus the numbers will be the squares of multiples of 11.

Thus the first number will be (1×11) × (1×11) = 11² = 121

The next candidate will be (2×11) × (2×11) = 22² = 484

The next possible candidate will be (3×11) × (3×11) = 33² = 1089 which is too large.

Thus there are two multiples of 11 less than 1000 whose square roots are whole numbers, namely 121 (11²) and 484 (22²)

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Q: How many Positive integers less than 1000 are multiples of 11 whose square roots are whole numbers?
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