1. **Problem statement:** There are 125 students arranged in rows such that the number of rows equals the number of students in each row. We need to find how many students are in each row. 2. **Understanding the problem:** If the number of rows is $n$ and the number of students in each row is also $n$, then the total number of students is given by the formula: $$\text{Total students} = n \times n = n^2$$ 3. **Given:** Total students = 125 4. **Set up the equation:** $$n^2 = 125$$ 5. **Solve for $n$:** $$n = \sqrt{125}$$ 6. **Simplify the square root:** $$\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}$$ 7. Since $n$ must be an integer (number of rows and students per row), and $5\sqrt{5}$ is not an integer, this means 125 is not a perfect square. 8. **Check if 125 can be arranged in such a way:** Since the problem states the number of rows equals the number of students per row, and 125 is not a perfect square, this is not possible. 9. **Conclusion:** There is no integer number of students per row such that the number of rows equals the number of students in each row for 125 students. 10. **Additional note:** The closest perfect squares near 125 are $11^2 = 121$ and $12^2 = 144$. So, if the problem requires an exact square arrangement, 125 students cannot be arranged in such a way. **Final answer:** There is no integer solution for the number of students per row if the number of rows equals the number of students in each row for 125 students.