Evaluate √3675x √2352 A sports teacher wants to arrange 6000 students in a field such that the number of rows. is equal to number of columns. Find the number of rows if 71 were left out after arrangement.
Answers
Answer:
1. Given,
√3675 × √2352
The factors of the above numbers are,
3675 = 3 × 5² × 7²
2352 = 2⁴ × 3 × 7²
√3675 × √2352
= √(3 × 5² × 7²) × √(2⁴ × 3 × 7²)
performing the square root, we get,
= ( √3 × 5 × 7 ) × ( 2² × √3 × 7 )
= (√3 × √3) × 2² × 5 × 7²
= 3 × 2² × 5 × 7²
= 3 × 4 × 5 × 49
= 60 × 49
= 2940
∴ √3675 × √2352 = 2940
2. Total number of students = 6000
Students are arranged in such a way that the number of row is equal to the number of columns
Due to this arrangement 71 students were left out
So, Number of students are in this arrangement = 6000-71
= 5929
Let x be the number of rows
Since no. of rows = No. of columns
So, No. of columns = x
So, x*x= 5929
x^2= 5929
x= root 5929
x= 77