Simplify Square Root of 25837

What is the square root of 25837 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.

√25837 = A√B

Unfortunately, the square root of 25837 cannot be simplified. Thus, here is the answer to the square root of 25837 in its simplest form:

√ 25837 = √ 25837

Here are two different methods we used to determine why the square root of 25837 cannot be simplified.

1) To be able to simplify the square root of 25837, one of the factors of 25837 other than 1 must be a perfect square. The factors of 25837 are 1, 7, 3691, and 25837. Since none of these factors are perfect squares, the square root of 25837 cannot be simplified.

2) To be able to simplify the square root of 25837, all the prime factors of 25837 cannot be unique. When we did prime factorization of 25837, we found that 7 x 3691 equals 25837. Since all the prime factors are unique, the square root of 25837 cannot be simplified.

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