# 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

(i) 252 :    Prime factorisation of 252 = .

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 = .

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 = .

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 = .

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 =

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 =

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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