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  • 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.

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)

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(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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Devendra Khairwa

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