Math and Arithmetic
Numbers

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

Top Answer
User Avatar
Wiki User
June 28, 2017 8:56PM

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)