Simplify Square Root of 55414

What is the square root of 55414 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.

√55414 = A√B

Unfortunately, the square root of 55414 cannot be simplified. Thus, here is the answer to the square root of 55414 in its simplest form:

√ 55414 = √ 55414

Here are two different methods we used to determine why the square root of 55414 cannot be simplified.

1) To be able to simplify the square root of 55414, one of the factors of 55414 other than 1 must be a perfect square. The factors of 55414 are 1, 2, 103, 206, 269, 538, 27707, and 55414. Since none of these factors are perfect squares, the square root of 55414 cannot be simplified.

2) To be able to simplify the square root of 55414, all the prime factors of 55414 cannot be unique. When we did prime factorization of 55414, we found that 2 x 103 x 269 equals 55414. Since all the prime factors are unique, the square root of 55414 cannot be simplified.

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