Simplify Square Root of 86303

What is the square root of 86303 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.

√86303 = A√B

Unfortunately, the square root of 86303 cannot be simplified. Thus, here is the answer to the square root of 86303 in its simplest form:

√ 86303 = √ 86303

Here are two different methods we used to determine why the square root of 86303 cannot be simplified.

1) To be able to simplify the square root of 86303, one of the factors of 86303 other than 1 must be a perfect square. The factors of 86303 are 1, 7, 12329, and 86303. Since none of these factors are perfect squares, the square root of 86303 cannot be simplified.

2) To be able to simplify the square root of 86303, all the prime factors of 86303 cannot be unique. When we did prime factorization of 86303, we found that 7 x 12329 equals 86303. Since all the prime factors are unique, the square root of 86303 cannot be simplified.

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