In a school, PT teacher wants to arrange 2000 students in form of rows and columns for PT display. If the number of rows is equal to the number of columns and 64 students can not accommodate this arrangement. find the number of rows.
Answers
Answer:
44
Step-by-step explanation:
We have a total of 2000 students. These students should be arranged in the form of rows and columns for P.T. Display.
We are given that the number of rows equals the number of columns.
64 students could not be accommodated in this arrangement.
So, Number of students in the arrangement =2000−64
Number of students in the arrangement =1936
Let x
denote the number of rows.
Since, Number of rows is equal to Number of Columns, we have
Number of rows =
Number of Columns
So, Number of Rows ×
Number of Columns =
Number of Students in the arrangement
Substituting the values in above equation, we get
⇒x⋅x=1936
⇒x2=1936
Taking Square root on both the sides, we have
⇒x=1936−−−−√
By factorization method, we have
⇒x=2×2×2×2×11×11−−−−−−−−−−−−−−−−−−√
⇒x=2×2×11
By multiplying the terms, we get
⇒x=44
Therefore, the number of rows where students are arranged for a P.T. Display is 44.
Note: Here we have found out the square root of 1936 using factorization method. We have two methods to find the square root of a number. If the number is small, it is quite easy to find the square root of a number. Any number can be expressed as a product of prime numbers. This method of representation of a number in terms of the product of prime numbers is termed as the prime factorization method.