Question

Question 5
Numbers given below are not perfect squares. Use prime factorization method to find the smallest number by which these can be divided to make them perfect squares.
(i) 1000
(ii) 867
(iii) 4375

Answer 1

Finding the smallest number by which the given numbers can be divided to make them perfect squares using prime factorization method:

• 1000 = 10 x 10 x 10

                 = (10 x 10) x 10

           After grouping the factors, we see that 10 has no pair so 1000 must be divided by 10 in order to make it a perfect square.

• 867 = 17 x 17 x 3

               = (17 x 17) x 3

           867 must be divided by 3 in order to make it a perfect square.

• 4375 = 5 x 5 x 5 x 5 x 7

                 = (5 x 5) x (5 x 5) x 7

            4375 must be divided by 7 to make it a perfect square