How many even numbers from 10 to 10,000 are not perfect squares (including both)?
Explanation:
The lowest such possible perfect square is 16 (42). The highest such possible perfect square is 10,000 itself (1002). ∴ The perfect squares are: 42, 62, ..., 1002 = (2 × 2)2, (2 × 3)2, ..., (2 × 50)2.
∴ Number of even perfect squares from 10 to 10,000 is (50 – 2 + 1) = 49.
Number of even numbers from 1 to 10,000 = 10,000/2 = 5000 Number of even numbers from 10 to 10,000 = 5000 - 4 = 4996 (excluding 2, 4, 6 and 8).
∴ Number of even numbers from 10 to 10,000 which are not perfect squares = 49996 - 49 = 4947.
Hence, 4947.
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