Simplify Square Root of 55555

What is the square root of 55555 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.

√55555 = A√B

Unfortunately, the square root of 55555 cannot be simplified. Thus, here is the answer to the square root of 55555 in its simplest form:

√ 55555 = √ 55555

Here are two different methods we used to determine why the square root of 55555 cannot be simplified.

1) To be able to simplify the square root of 55555, one of the factors of 55555 other than 1 must be a perfect square. The factors of 55555 are 1, 5, 41, 205, 271, 1355, 11111, and 55555. Since none of these factors are perfect squares, the square root of 55555 cannot be simplified.

2) To be able to simplify the square root of 55555, all the prime factors of 55555 cannot be unique. When we did prime factorization of 55555, we found that 5 x 41 x 271 equals 55555. Since all the prime factors are unique, the square root of 55555 cannot be simplified.

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