Certainly! Let's tackle the problem step by step.
### Part i) How many students are there in each row?
Since 400 students are assembled in a square form, we can determine the number of students in each row by finding the square root of the total number of students.
- Total number of students: 400
Finding the square root of 400:
[tex]\[ \sqrt{400} = 20 \][/tex]
So, there are 20 students in each row.
### Part ii) How many students are taken out from each row if there are 324 students left in the assembly?
We know that there are initially 400 students and they are arranged in a perfect square with 20 students per row. After some students are taken out, 324 students remain. To determine the number of students per row now, we find the square root of 324:
[tex]\[ \sqrt{324} = 18 \][/tex]
Initially, there were 20 students per row. Now there are 18 students per row. To find the number of students taken out from each row:
[tex]\[ 20 - 18 = 2 \][/tex]
So, 2 students are taken out from each row.
### Part iii) How many more students are required so that there is 1 more student each row than the original number of students?
Initially, there are 20 students in each row. We need to find out how many students are required to make it so there are 21 students per row. If there are 21 students per row in a square formation, we need the total number of students to be:
[tex]\[ 21^2 = 441 \][/tex]
The original number of students is 400. The additional students required:
[tex]\[ 441 - 400 = 41 \][/tex]
Therefore, 41 more students are needed so that there is 1 more student in each row than the original number of students.
