Simplify Square Root of 82201

What is the square root of 82201 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.

√82201 = A√B

Unfortunately, the square root of 82201 cannot be simplified. Thus, here is the answer to the square root of 82201 in its simplest form:

√ 82201 = √ 82201

Here are two different methods we used to determine why the square root of 82201 cannot be simplified.

1) To be able to simplify the square root of 82201, one of the factors of 82201 other than 1 must be a perfect square. The factors of 82201 are 1, 7, 11743, and 82201. Since none of these factors are perfect squares, the square root of 82201 cannot be simplified.

2) To be able to simplify the square root of 82201, all the prime factors of 82201 cannot be unique. When we did prime factorization of 82201, we found that 7 x 11743 equals 82201. Since all the prime factors are unique, the square root of 82201 cannot be simplified.

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