Simplify Square Root of 52826

What is the square root of 52826 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.

√52826 = A√B

Unfortunately, the square root of 52826 cannot be simplified. Thus, here is the answer to the square root of 52826 in its simplest form:

√ 52826 = √ 52826

Here are two different methods we used to determine why the square root of 52826 cannot be simplified.

1) To be able to simplify the square root of 52826, one of the factors of 52826 other than 1 must be a perfect square. The factors of 52826 are 1, 2, 61, 122, 433, 866, 26413, and 52826. Since none of these factors are perfect squares, the square root of 52826 cannot be simplified.

2) To be able to simplify the square root of 52826, all the prime factors of 52826 cannot be unique. When we did prime factorization of 52826, we found that 2 x 61 x 433 equals 52826. Since all the prime factors are unique, the square root of 52826 cannot be simplified.

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