A new sequence is obtained from the sequence of positive integers (1,2,3,…) by deleting all the perfect squares. Then the 2022nd term of the new sequence is ________.
Explanation:
2022nd number in the sequence (including perfect squares) is 2022.
Now let us calculate number of perfect squares till 2022.
12, 22, 32, 42, 52, ..., 442 i.e., 44 numbers.
∴ 2022nd number will be 2022 + 44 = 2066.
Here we need to check if there is any perfect square between 2022 and 2066. 2025 i.e., 452 is a perfect square between 2022 and 2066.
⇒ 2022nd number in the given sequence after removing perfect squares will be 2067.
Hence, 2067.
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