Step-by-step explanation:



(i) Resolving 1575 into PRIME factors:

Thus, to get a perfect SQUARE, the given number should be divided by 7

New number obtained

Hence, the new number is the square of 15

(ii) Resolving 9075 into prime factors: 

Thus, to get a perfect square, the given number should be divided by 3

New number obtained

Hence, the new number is the square of  55

(iii) Resolving 4851 into prime factors:

Thus, to get a perfect square, the given number should be divided by 11

New number obtained

Hence, the new number is the square of 21

(iv) Resolving 3380 into prime factors: 

Thus, to get a perfect square, the given number should be divided by 5

New number obtained

Hence, the new number is the square of 26

(v) Resolving 4500 into prime factors: 

Thus, to get a perfect square, the given number should be divided by 5

New number obtained

Hence, the new number is the square of 30

(vi) Resolving 7776 into prime factors:

Thus, to get a perfect square, the given number should be divided by 6 whish is a PRODUCT of 2 and 3

New number obtained

Hence, the new number is the square of 36

(VII) Resolving 8820 into prime factors:

Thus, to get a perfect square, the given number should be divided by 5

New number obtained

Hence, the new number is the square of 42

(viii) Resolving 4056 into prime factors: 

Thus, to get a perfect square, the given number should be divided by 6, which is a product of 2 and 3

New number obtained

Hence, the new number is the square of 26