Simplify Square Root of 39162

What is the square root of 39162 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.

√39162 = A√B

Unfortunately, the square root of 39162 cannot be simplified. Thus, here is the answer to the square root of 39162 in its simplest form:

√ 39162 = √ 39162

Here are two different methods we used to determine why the square root of 39162 cannot be simplified.

1) To be able to simplify the square root of 39162, one of the factors of 39162 other than 1 must be a perfect square. The factors of 39162 are 1, 2, 3, 6, 61, 107, 122, 183, 214, 321, 366, 642, 6527, 13054, 19581, and 39162. Since none of these factors are perfect squares, the square root of 39162 cannot be simplified.

2) To be able to simplify the square root of 39162, all the prime factors of 39162 cannot be unique. When we did prime factorization of 39162, we found that 2 x 3 x 61 x 107 equals 39162. Since all the prime factors are unique, the square root of 39162 cannot be simplified.

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