Q.5  For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained

(i) 252

(ii) 180

(iii) 1008

(iv) 2028

(v) 1458

(vi) 768

Answers (1)

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

               To make pairs we will multiply 252 with 7.

               So the number is 1764 and its square root is 42.

 

(ii) 180 :     Prime factorisation of 180 = 2\times2\times3\times3\times5.

                 To make it perfect square, multiply by 5.

                 So the number is 900 and its square root is 30.

 

(iii) 1008 :   Prime factorization of 1008 gives = 2\times2\times2\times2\times3\times3\times7.

                 To make pairs we need to multiply it by 7.

                 So the number we get is 7056 and its square root is 84.

 

(iv) 2028 :    Prime factorisation of 2028 = 2\times2\times3\times13\times13.

                  To make pairs we multiply the number by 3.

                  So the number obtained is 6084 and its square root is 78.

 

(v)  1458 :   Prime factorisation of 1458 gives = 2\times3\times3\times3\times3\times3\times3

                  To make pairs we need to multiply the number by 2.

                  So the number obtained is 2916 and its square root is 54.

 

(vi) 768  :     Prime factorisation of 768 gives = 2\times2\times2\times2\times2\times2\times2\times3

                   To make pairs we need to multiply the given number by 6.

                   So the required number is 4608 and its square root is 48.

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