(i) 484
Resolving 484 into prime factors we get,
484 = 2 × 2 × 11 × 11
Now,
Grouping the factors into pairs of equal factors, we get:
484 = (2 × 2) × (11 × 11)
We observe that all are paired so,
484 is a perfect square
(ii) 625
Resolving 625 into prime factors we get,
625 = 5 × 5 × 5 × 5
Now,
Grouping the factors into pairs of equal factors, we get:
625 = (5 × 5) × (5 × 5)
We observe that all are paired so,
625 is a perfect square
(iii) 576
Resolving 576 into prime factors we get,
576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
Now,
Grouping the factors into pairs of equal factors, we get:
576 = (2 × 2) × (2 × 2) × (2 × 2) × (3 × 3)
We observe that all are paired so,
576 is a perfect square
(iv) 941
Resolving 941 into prime factors we get,
941 = 941 × 1
Now,
As 941 itself is a prime number
Hence,
It do not have a perfect square
(v) 961
Resolving 961 into prime factors we get,
961 = 31 × 31
Now,
Grouping the factors into pairs of equal factors, we get:
961 = (31 × 31)
We observe that all are paired so,
961 is a perfect square
(vi) 2500
Resolving 2500 into prime factors we get,
2500 = 2 × 2 × 5 × 5 × 5 × 5
Now,
Grouping the factors into pairs of equal factors, we get:
2500 = (2 × 2) × (5 × 5) × (5 × 5)
We observe that all are paired so,
2500 is a perfect square
