Q. 53.9( 118 Votes )

For each of the f

Answer :

(i)The prime factorization of 252 is follows:

252 = 2 × 2 × 3 × 3 × 7

Here,

Prime factor 7 does not have its pair.


If 7 gets a pair, then the number will become a perfect square.

Therefore, 252 has to be multiplied with 7 to obtain a perfect square

252 × 7 = 2 × 2 × 3 × 3 × 7 × 7

Hence,

252 × 7 = 1764 is a perfect square


2 * 3 * 7


= 42


(ii) The prime factorization of 180 is as follows:


180 = 2 × 2 × 3 × 3 × 5


Here, prime factor 5 does not have its pair.


If 5 gets a pair, then the number will become a perfect square.


Therefore, 180 has to be multiplied with 5 to obtain a perfect square.


180 × 5 = 900 = 2 × 2 × 3 × 3 × 5 × 5


Therefore,


180 × 5 = 900 is a perfect square


= 2 * 3 * 5


= 30


(iii) The prime factorization of 1008 isas follows:


1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7


Here, prime factor 7 does not have its pair.


If 7 gets a pair, then the number will become a perfect square.


Therefore, 1008 can be multiplied with 7 to obtain a perfect square.


1008 × 7 = 7056 = 2 × 2 ×2 × 2 × 3 × 3 × 7 × 7


Therefore,


1008 × 7 = 7056 is a perfect square


= 2 * 2 * 3 * 7


= 84


(iv) The prime factorization of 2028 is as follows:


2028 = 2 * 2 * 3 * 13 * 13


Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 2028 can be multiplied with 3 to obtain a perfect square.


2028 × 3 = 6084 = 2 × 2 ×3 × 3 × 13 × 13


Therefore,


2028 × 3 = 6084 is a perfect square


= 2 * 3 * 13


= 78


(v) The prime factorization of 1458 is as follows:


1458 = 2 * 3 * 3 * 3 * 3 * 3 * 3


Here, prime factor 2 does not have its pair.


If 2 gets a pair, then the number will become a perfect square.


Therefore, 1458 can be multiplied with 2 to obtain a perfect square.


1458 × 2 = 2916 = 2 × 2 ×3 × 3 × 3 × 3 × 3 × 3


Therefore,


1458 × 2 = 2916 is a perfect square


= 2 * 3 * 3 * 3


= 54


(vi) The prime factorization of 768 is as:


768 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3


Here, prime factor 3 does not have its pair.


If 3 gets a pair, then the number will become a perfect square.


Therefore, 768 can be multiplied with 3 to obtain a perfect square.


768 × 3 = 2304 = 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 ×3 ×3


Therefore,


768 × 3 = 2304 is a perfect square


= 2 * 2 * 2 * 2 * 3


= 48

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