Using prime factorization method. find which of the following number are perfect square
Answers
Step-by-step explanation:
The given numbers are 189, 225, 2048, 343, 441, 2916, 11025, 3549.
(1) Representing 189 as the product of its prime factors,
189=3
2
×3×7
Since, it does not have equal pairs of factors, it is not a perfect square.
∴ 189 is not a perfect square.
(2) Representing 225 as the product of its prime factors,
225=(5×5)×(3×3)
Since 225 has equal pairs of factors, it is a perfect square.
∴ 225 is a perfect square.
(3) Representing 2048 as the product of its prime factors,
2048=(2×2)×(2×2)×(2×2)×(2×2)×(2×2)×2
Since 2048 does not have equal pairs of factors, it is not a perfect square.
∴ 2048 It is a not a perfect square.
(4) Representing 343 as the product of its prime factors,
343=(7×7)×7
Since 343 does not have equal pairs of factors, it is not a perfect square.
∴ 343 is not a perfect square.
(5) Representing 441 as the product of its prime factors,
441=(7×7)×(3×3)
Since 441 has equal pairs of factors, it is a perfect square.
∴ 441 is a perfect square.
(6) Representing 2916 as the product of its prime factors,
2916=(3×3)×(3×3)×(3×3)×(2×2)
Since 2961 has equal pairs of factors, it is a perfect square.
∴ 2916 is a perfect square.
(7) Representing 11025 as the product of its prime factors,
11025=(3×3)×(5×5)×(7×7)
Since 11025 has equal pairs of factors, it is a perfect square.
∴ 11025 is a perfect square.
(8) Representing 3549 as the product of its prime factors,
3549=(13×13)×3×7
Since 3549 does not have equal pairs of factors, it is not a perfect square.
∴ 3549 It is a not a perfect square.
Hence, out of all the given numbers, 225, 441, 2916 and 11025 are perfect squares.