Question

Find the smallest natural number by which 5808 should be divided to make it a perfect
square. Also, find the number whose square is the resulting number.


Explain Properly​

Answer 1

Process : We prime factorise the number 5808 in order to find the smallest natural number by which it should be divided to make it a perfect square where we will see one or more unpaired numbers.

Solution :

The given number is 5808

Now, 5808

= 2 × 2904

= 2 × 2 × 1452

= 2 × 2 × 2 × 726

= 2 × 2 × 2 × 2 × 363

= 2 × 2 × 2 × 2 × 3 × 121

= 2 × 2 × 2 × 2 × 3 × 11 × 11

We see that the only unpaired prime number is 3 and thus this is the smallest number by which 5808 should be divided to get the perfect square.

The required perfect square is

= 2 × 2 × 2 × 2 × 11 × 11

= 1936, which is the square of 44