Let Sᵢ denote the set of all integers n such that 100i ≤ n < 100(i+1). For example S₄ contains 400,401, 402, 403,...,499. How many such sets from S₀ to S₉₉₉ do not contain a perfect square.

Number Theory question

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$$\text{Let } S_i \text{ denote the set of all integers n such that } 100i\leq n \lt 100(i+1). \\ \text{For example } S_4 \text{ contains } 400,401, 402, 403,...,499. \\\text{ How many such sets from } S_0 \text{ to } S_{999} \text{ do not contain a perfect square.}$$

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