Simplify Square Root of 39354

What is the square root of 39354 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.

√39354 = A√B

Unfortunately, the square root of 39354 cannot be simplified. Thus, here is the answer to the square root of 39354 in its simplest form:

√ 39354 = √ 39354

Here are two different methods we used to determine why the square root of 39354 cannot be simplified.

1) To be able to simplify the square root of 39354, one of the factors of 39354 other than 1 must be a perfect square. The factors of 39354 are 1, 2, 3, 6, 7, 14, 21, 42, 937, 1874, 2811, 5622, 6559, 13118, 19677, and 39354. Since none of these factors are perfect squares, the square root of 39354 cannot be simplified.

2) To be able to simplify the square root of 39354, all the prime factors of 39354 cannot be unique. When we did prime factorization of 39354, we found that 2 x 3 x 7 x 937 equals 39354. Since all the prime factors are unique, the square root of 39354 cannot be simplified.

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