Question

Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers.

Answer 1

10368 = `bar(2xx2) xx bar(2xx2) xx bar(2xx2) xx2 xx bar(3xx3) xx bar(3xx3)`

On grouping the prime factors of 10368 as shown; one factors i.e. 2 is left which cannot be paired with equal factor.

2	10368
2	5184
2	2592
2	1296
2	648
2	324
2	162
3	81
3	27
3	9
	3

 

 

 

 

 

 

 

 

 

 

 

∴ The given number should be divided by 2.

Now `sqrt(10368/2)`

= `sqrt((bar(2xx2) xxbar(2xx2) xx bar(2xx2) xx2 xx bar(3xx3) xx bar(3xx3))/(2)`

= 2 x 2 x 2 x 3 x 3 = 72