# [Solved] A yoga instructor wants to arrange the maximum possible number of 6000 students in a ground so that the number of rows is the same as the number of columns. How many rows will be there if 71 students are left out after the arrangement?

**A yoga instructor wants to arrange a maximum possible number of 6000 students in a ground so that the number of rows is the same as the number of columns. How many rows will be there if 71 students are left out after the arrangement?**

**Concept used:**

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2 because 2 * 2 = 4.

In this question, we are trying to find the value of n, which is the number of rows in the grid. We know that n^2 is the number of squares in the grid, and that the number of squares is equal to the number of students we have left to place (5929).

To find the value of n, we can take the square root of both sides of the equation n^2 = 5929. The square root of n^2 is n, so this allows us to solve for n. Once we find the value of n, we know that there are n rows in the grid.

**Step by Step Explanation**

- We are given a ground that a yoga instructor wants to fill with 6000 students, and we want to find the number of rows of students that will be in the ground.
- To maximize the number of students that can be seated in the ground, the ground should be arranged in a square shape with an equal number of rows and columns.
- The number of students that can be seated in the ground can be calculated by finding the square of the number of rows. If there are N rows, then the number of students that can be seated in the ground is N^2.
- Since we know that there are 6000 students, we can set up the equation N
^{2}= 6000. - We can solve for N by taking the square root of both sides of the equation. This gives us N = √6000.
- Since the number of rows must be an integer, we can round down to the nearest integer to get N = 77.
- We are also told that there are 71 students left over after the arrangement. This means that there must be 6 rows with 71 students.

Therefore, the number of rows in the ground is 77.

- First, we are given that there are 6000 students and we want to arrange them in a grid with the same number of rows and columns.
- Let’s say there are n rows and n columns. This means that we can place the students in n^2 squares.
- We are also told that 71 students are left out after the arrangement. This means that we have 6000 – 71 = 5929 students to place in the grid.
- We want to find the value of n, which is the number of rows and columns in the grid. To do this, we can set up an equation where n^2 is equal to the number of students we have left to place, which is 5929.
- To solve for n, we can take the square root of both sides of the equation. The square root of n^2 is n, so the equation becomes:√n^2 = √5929
- We can simplify this equation to get:n = √5929
- The square root of 5929 is approximately 77. This means that there are 77 rows in the grid.