(i) Given 441, A perfect square can always be expressed as a product of pairs of equal factors.Now resolve 441 into prime factors, we get 441 = 49 X 9
= 7 X 7 X 3 X 3
= 7 X 3 X 7 X 3
= 21 X 21
= (21)2
Hence, 21 is the number whose square is 441
∴ 441 is a perfect square.
(ii) Given 576 A perfect square can always be expressed as a product of pairs of equal factors.Now resolve 576 into prime factors, we get 576 = 64 X 9
= 8 X 8 X 3 X 3
= 8 X 3 X 8 X 3
= 24 X 24
= (24)2
Hence, 24 is the number whose square is 576
∴ 576 is a perfect square.
(iii) Given 11025 A perfect square can always be expressed as a product of pairs of equal factors.Now resolve 11025 into prime factors, we get 11025 = 441 X 25
= 49 X 9
= 7 X 7 X 3 X 3 X 5 X 5
= 7 X 3 X 5 X 7 X 3 X 5
= 105 X 105
= (105)2
Hence, 105 is the number whose square is 11025
∴ 11025 is a perfect square.
(iv) Given 1176 A perfect square can always be expressed as a product of pairs of equal factors.Now resolve 1176 into prime factors, we get 1176 = 7 X 168
Again resolve 168 into prime factors we get,
1176 = 7 X 168
= 7 X 21 X 8
= 7 X 7 X 3 X 2 X 2 X 2
1176 cannot be expressed as a product of two numbers.
Thus 1176 is not a perfect square.