Answer :

(i) 1156


Resolving 1156 into prime factors we get,


1156 = 2 × 2 × 17 × 17


Now, grouping the factors into pairs of equal factors


We get,


1156 = (2 × 2) × (17 × 17)


As all factors are paired


Hence, 1156 is a perfect square


Again,


1156 = (2 × 17) × (2 × 17)


= 34 × 34


= (34)2


Thus, 1156 is a square of 34


(ii) 2025


Resolving 2025 into prime factors we get,


2025 = 3 × 3 × 3 × 3 × 5 × 5


Now, grouping the factors into pairs of equal factors


We get,


2025 = (3 × 3) × (3 × 3) × (5 × 5)


As all factors are paired


Hence, 2025 is a perfect square


Again,


2025 = (3 × 3 × 5) × (3 × 3 × 5)


= 45 × 45


= (45)2


Thus, 2025 is a square of 45


(iii)14641


Resolving 14641 into prime factors we get,


14641 = 11 × 11 × 11 × 11


Now, grouping the factors into pairs of equal factors


We get,


14641 = (11 × 11) × (11 × 11)


As all factors are paired


Hence, 14641 is a perfect square


Again,


14641 = (11 × 11) × (11 × 11)


= 121 × 121


= (121)2


Thus, 14641 is a square of 121


(iv) 4761


Resolving 4761 into prime factors we get,


4761 = 3 × 3 × 23 × 23


Now, grouping the factors into pairs of equal factors


We get,


4761 = (3 × 3) × (23 × 23)


As all factors are paired


Hence, 4761 is a perfect square


Again,


4761 = (3 × 23) × (3 × 23)


= 69 × 69


= (69)2


Thus, 4761 is a square of 69


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