Question

Find the least positive integer which should be multiplied to 720 so that the product obtained is a perfect square

Answer 1

We can write

720 = 2*2*2*2*3*3*5

In order to be a perfect square a number must contain one prime factor twice.
Hence,clearly 5 is not in pair.So, 5 is the least positive integer which should be multiplied to 720 so that the product obtained is a perfect square.

Answer 2

here we have.....the number 720.
when we take the prime factors if 720 we get=5*2*2*2*2*3*3
as we know that in square of a number we have pairs.....that is of 2

so likewise...here also in the prime factor we will take a pair of each number
=5*[2*2]*[2*2]*[3*3]
here we found that we got a pair of each number except for 5

to make a pair for 5 we need one more 5=5*5

so the least positive num. we need is 5
=720*5=3600
and 3600 is a perfect square of 60.