367. Valid Perfect Square 

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class Solution {
    public boolean isPerfectSquare(int num) {
        int left = 1, right = num;
        int ans = 0;
        while (left <= right) {
            int mid = (left + right) >>> 1;
            if (mid <= num / mid) {
                ans = mid;
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }

        return ans * ans == num;
    }
}

Math

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class Solution {
    public boolean isPerfectSquare(int num) {
        int x = 1;
        while (num > 0) {
            num -= x;
            x += 2;
        }

        return num == 0;
    }
}

References

367. Valid Perfect Square