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# 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

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

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(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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