there are 1250 children in a school. for a PT drill they have to stand in such in such a way that number of rows is equal to number of columns .how many children are left out of the arrangement
Answers
Answer:
Number of children left out are 25.
Step-by-step explanation:
Total number of children in the school = 1250 children
Let the number of rows the children stand in = x rows
According to question, number of rows = number of columns
Hence, Number of columns = x columns
If we have an arrangement of x rows and x columns,
The total children that can fit in = x^2
x^2 <= 1250
(we need to find the highest perfect square less than or equal to 1250)
x <= 35.35
(by using long division method to find square root of 1250)
(x is strictly an integer, rows cant be decimal values)
the nearest smaller integer = 35
x^2 = (35)^2
= 1225
Hence, 1225 children can stand in an arrangement of x rows and x columns.
Children left out = total children - children that can be arranged
= 1250 - 1225
= 25 children
25 children are left out of the arrangement.
Step-by-step explanation:
Tip. Since the children have to stand in such a way that the number of rows is equal to the number of columns, we find the square root of 1250.
Prime factorization gives 1250 = 2 × 5 × 5 × 5 × 5
So, √1250 = 5 × 5 × √2 = 25√2 = 35.35...
Thus the number of required rows = the number of required columns = 35
Now, the number of children required for the PT drill
= 35 × 35 (or, 35²)
= 1225
So, the number of children left out
= 1250 - 1225
= 25
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