Simplify Square Root of 52806

What is the square root of 52806 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.

√52806 = A√B

Unfortunately, the square root of 52806 cannot be simplified. Thus, here is the answer to the square root of 52806 in its simplest form:

√ 52806 = √ 52806

Here are two different methods we used to determine why the square root of 52806 cannot be simplified.

1) To be able to simplify the square root of 52806, one of the factors of 52806 other than 1 must be a perfect square. The factors of 52806 are 1, 2, 3, 6, 13, 26, 39, 78, 677, 1354, 2031, 4062, 8801, 17602, 26403, and 52806. Since none of these factors are perfect squares, the square root of 52806 cannot be simplified.

2) To be able to simplify the square root of 52806, all the prime factors of 52806 cannot be unique. When we did prime factorization of 52806, we found that 2 x 3 x 13 x 677 equals 52806. Since all the prime factors are unique, the square root of 52806 cannot be simplified.

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