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: 

1156 

Answer 1

In  problem, factorise the number into its prime factor 

1156 = 2 x 2 x 17 x 17
Grouping the factors into pairs of equal factors, we obtain:
1156 = (2 x 2) x (17 x 17)
No factors are left over. Hence, 1156 is a perfect square. Moreover, by grouping 1156 into equal factors:
1156 = (2 x 17) x (2 x 17)
         = (2 x 17)²
Hence, 1156 is the square of 34, which is equal to 2 x 17.