Question

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case: 

 4761 

Answer 1

In  problem, factorise the number into its prime factor. 

 4761 = 3 x 3 x 23 x 23
Grouping the factors into pairs of equal factors, we obtain:
4761 = (3 x 3) x (23 x 23)
No factors are left over. Hence, 4761 is a perfect square. The above expression is already grouped into equal factors:
4761 = (3 x 23) x (3 x 23)
            = (3 x 23)²
Hence, 4761 is the square of 69, which is equal to 3 x 23.