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:

 14641 

 

Answer 1

In  problem, factorise the number into its prime factor. 

14641 = 11 x 11 x 11 x 11
Grouping the factors into pairs of equal factors, we obtain:
14641 = (11 x 11) x (11 x 11)
No factors are left over. Hence, 14641 is a perfect square. The above expression is already grouped into equal factors:
14641 = (11 x 11) x (11 x 11)
            = (11 x 11)²
Hence, 14641 is the square of 121, which is equal to 11 x 11.