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.