Final answer:
To find the smallest number by which 540 must be multiplied for a perfect square, factorize 540 and ensure all prime factors have even powers. The result is 900.
Step-by-step explanation:
To find the smallest number by which 540 must be multiplied so that the product is a perfect square, we need to factorize 540.
540 can be factorized as 2^2 x 3^3 x 5.
In order for the product to be a perfect square, we need to realize that all the powers of the prime factors in the factorization must be even.
Therefore, the smallest number by which 540 must be multiplied to obtain a perfect square is (2 x 3 x 5)^2, which is 30^2 = 900.
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