Q.6 For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.

(i) 252

(ii) 2925

(iii) 396

(iv) 2645

(v) 2800

(vi) 1620

 

Answers (1)

(i) 252: Prime factorization of 252 gives = 2\times2\times3\times3\times7.

                 For making pairs we will divide the given number by 7.

                 The obtained number is 36 and its square root is 6.

(ii) 2925: Prime factorization of 2925 gives = 3\times3\times5\times5\times13

                  To make pairs divide the given number by 13.

                  So the obtained number is 225 and its square root is 15.

(iii) 396: Prime factorization if 396 = 2\times2\times3\times3\times11

                   For obtaining perfect square number we need to divide the given number by 11.

                  So the required number is 36 and its square root is 6.

(iv) 2645: Prime factorization of 2645 = 5\times23\times23

                    We need to divide the given number by 5 to obtain the perfect square number.

                    So the obtained number is 529 and its square root is 23.

(v) 2800:      Prime factorization of 2800  =  2\times2\times2\times2\times5\times5\times7

                     To make pairs we need to divide 2800 by 7.

                    So the required number is 400 and its square root is 20.

(vi) 1620: Prime factorization of 1620 gives = 2\times2\times3\times3\times3\times3\times5

                    To make pairs divide the given number by 5.

                   We get , number = 324 and its square root = 18.

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