ruplun wrote:If n^2 is divisible by 72,what is the largest possible number that must divide n?

Picking Number Approach
Least possible value of n² such that n² is divisible by 72 is 72*2 = 144
Hence, minimum possible value of n = 12.
Largest possible integer that divides n is 12.


Algebraic Approach:
n² is divisible by 72
Hence we can write n² as 72k, where k is an positive integer.
Now, n = √n² = √(72k) = √[(2)*(36)*k] = 6√(2k)
Now for n to be an integer, k must be an even multiple of a perfect square.
Hence, we can write k = 2m², where is a positive integer.
Now, n = 6√(2k) = 6√(2*2*m²) = 12m

Hence, largest possible integer that divides n is 12.