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The smallest number by which 396 must be multiplied so that the product becomes a perfect square is:

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answer is B.

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Detailed Solution

Given number is 396.
Writing the prime factors of the number 369,

396 = 2 \times 2 \times 3 \times 3 \times 11

Multiplying 396 by 11 to obtain a perfect square as prime factor 11 does not have a pair.

396 \times 11 = 4356

4356 is a perfect square of the number 66.
So, 396 should be multiplied by 11 to make the product a perfect square.
Therefore, option (2) is correct.

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