Simplify Square Root of 46443

What is the square root of 46443 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√46443 = A√B

Unfortunately, the square root of 46443 cannot be simplified. Thus, here is the answer to the square root of 46443 in its simplest form:

√ 46443 = √ 46443

Here are two different methods we used to determine why the square root of 46443 cannot be simplified.

1) To be able to simplify the square root of 46443, one of the factors of 46443 other than 1 must be a perfect square. The factors of 46443 are 1, 3, 113, 137, 339, 411, 15481, and 46443. Since none of these factors are perfect squares, the square root of 46443 cannot be simplified.

2) To be able to simplify the square root of 46443, all the prime factors of 46443 cannot be unique. When we did prime factorization of 46443, we found that 3 x 113 x 137 equals 46443. Since all the prime factors are unique, the square root of 46443 cannot be simplified.

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