Simplify Square Root of 82247

What is the square root of 82247 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.

√82247 = A√B

Unfortunately, the square root of 82247 cannot be simplified. Thus, here is the answer to the square root of 82247 in its simplest form:

√ 82247 = √ 82247

Here are two different methods we used to determine why the square root of 82247 cannot be simplified.

1) To be able to simplify the square root of 82247, one of the factors of 82247 other than 1 must be a perfect square. The factors of 82247 are 1, 11, 7477, and 82247. Since none of these factors are perfect squares, the square root of 82247 cannot be simplified.

2) To be able to simplify the square root of 82247, all the prime factors of 82247 cannot be unique. When we did prime factorization of 82247, we found that 11 x 7477 equals 82247. Since all the prime factors are unique, the square root of 82247 cannot be simplified.

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