Simplify Square Root of 39223

What is the square root of 39223 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.

√39223 = A√B

Unfortunately, the square root of 39223 cannot be simplified. Thus, here is the answer to the square root of 39223 in its simplest form:

√ 39223 = √ 39223

Here are two different methods we used to determine why the square root of 39223 cannot be simplified.

1) To be able to simplify the square root of 39223, one of the factors of 39223 other than 1 must be a perfect square. The factors of 39223 are 1, 61, 643, and 39223. Since none of these factors are perfect squares, the square root of 39223 cannot be simplified.

2) To be able to simplify the square root of 39223, all the prime factors of 39223 cannot be unique. When we did prime factorization of 39223, we found that 61 x 643 equals 39223. Since all the prime factors are unique, the square root of 39223 cannot be simplified.

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