Question

find the least no. by which 10368 should be increased to make it a perfect square
give step by step explanation​

Answer 1

Notice that 10368 is greater than 100^2.

Identification like such is crucial to solving such problems.

Let us consider 101^2. It is equal to 10201.(<10368)

Let us consider 102^2.It is equal to 10404.(>10368)

Therefore, 10368 lies between 101^2 and 102^2.

Since it is required to find the number which must be ADDED to 10368 to make it a perfect square, consider 102^2=10404

10404-10368=36.

Hence, 36 is the answer.

If the question had asked for least no. by which 10368 must be decreased to make it a perfect square,

we would have taken 101^2=10201

and answer would have been 10368-10201=167

Answer 2

Answer:

Step-by-step explanation:

The prime factors of 10368 are:

 10368  =  2*2*2*2*2*2*2*3*3*3*3

 

 10368  =  ( (2*2*2)*(3*3) ) * ( (2*2*2*2)*(3*3) )

 

Rule to remember:  Perfect squares have an even number of each prime factor.

 

 

We can make a perfect square by multiplying bt 2 (the least prime factor that appears an odd number of times).

  20736 = ( (2* 2*2*2)*(3*3) ) * ( (2*2*2*2)*(3*3) )

 

Or, we can divide it by 2 (the least prime factor that appears an odd number of times).

  5184 = ( (2*2*2)*(3*3) ) * ( (    2*2*2)*(3*3) )

 

Since SQRT(10368) = 101.82  is between 101*101=10201  and 102*102=10404,  (the nearest perfect squares),

 

we may add 36  to get 10404,