Question

Using prime factorisation method find which of the following number are perfect square 189,225,343,441,2048,2916,3549,11028

Answer 1

Answer:

189 prime factors are

189=32×3×7

Since, it does not have equal pairs of factors.

∴ 189 is not a perfect square.

225 prime factors are

225=(5×5)×(3×3)

Since 225 has equal pairs of factors.

∴  It is a perfect square.

2048 prime factors are

2048=(2×2)×(2×2)×(2×2)×(2×2)×(2×2)×2

Since 2048 does not have equal pairs of factors.

∴  It is a not a perfect square.

441 prime fators are

441=(7×7)×(3×3)

Since 441 has equal pairs of factors.

∴  It is a perfect square.

2961 prime factors are

2961=(3×3)×(3×3)×(3×3)×(2×2)

Since 2961 has equal pairs of factors.

∴  It is a perfect square.

11025 prime factors are

11025=(3×3)×(5×5)×(7×7)

Since 11025 has equal pairs of factors.

∴  It is a perfect square.

3549 prime factors are

3549=(13×13)×3×7

Since 3549 does not have equal pairs of factors.

∴  It is a not a perfect square.