Orchard Tree Calculation
The problem states there are 5776 trees in an orchard. The arrangement is such that the number of rows is equal to the number of trees in each row. We need to find the number of rows.
Mathematical Representation
Let R be the number of rows.
According to the problem, the number of trees in each row is also R.
The total number of trees is the product of the number of rows and the number of trees per row.
Total Trees = (Number of Rows) $\times$ (Number of Trees per Row)
$ 5776 = R \times R $
$ 5776 = R^2 $
Finding the Number of Rows
To find the number of rows (R), we need to calculate the square root of the total number of trees.
$ R = \sqrt{5776} $
We can estimate the square root:
- $70^2 = 4900$
- $80^2 = 6400$
- Since 5776 is between 4900 and 6400, the square root is between 70 and 80.
- The last digit of 5776 is 6. The square root must end in 4 or 6 (since $4^2=16$ and $6^2=36$).
- Let's test 76: $76 \times 76 = 5776$.
Therefore, R = 76.
Conclusion
The number of rows in the orchard is 76.
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