Simplify Square Root of 55634

What is the square root of 55634 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.

√55634 = A√B

Unfortunately, the square root of 55634 cannot be simplified. Thus, here is the answer to the square root of 55634 in its simplest form:

√ 55634 = √ 55634

Here are two different methods we used to determine why the square root of 55634 cannot be simplified.

1) To be able to simplify the square root of 55634, one of the factors of 55634 other than 1 must be a perfect square. The factors of 55634 are 1, 2, 27817, and 55634. Since none of these factors are perfect squares, the square root of 55634 cannot be simplified.

2) To be able to simplify the square root of 55634, all the prime factors of 55634 cannot be unique. When we did prime factorization of 55634, we found that 2 x 27817 equals 55634. Since all the prime factors are unique, the square root of 55634 cannot be simplified.

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