Question

Is 33075 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.​

Answer 1

Prime factorising 33275, we get,

33275=5×5×11×11×11

=5 2 ×11 3 .

We know, a perfect cube has multiples of 3 as powers of prime factors.

• Here, number of 5's is 2 and number of 11's is 3.
• So we need to multiply another 5 to the factorization to make 33275 a perfect cube.
• Hence, the smallest number by which 33275 must be multiplied to obtain a perfect cube is 5.

Answer 2

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3 should be multiplied to get a perfect square

105 is the new number