Simplify Square Root of 43126

What is the square root of 43126 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.

√43126 = A√B

Unfortunately, the square root of 43126 cannot be simplified. Thus, here is the answer to the square root of 43126 in its simplest form:

√ 43126 = √ 43126

Here are two different methods we used to determine why the square root of 43126 cannot be simplified.

1) To be able to simplify the square root of 43126, one of the factors of 43126 other than 1 must be a perfect square. The factors of 43126 are 1, 2, 21563, and 43126. Since none of these factors are perfect squares, the square root of 43126 cannot be simplified.

2) To be able to simplify the square root of 43126, all the prime factors of 43126 cannot be unique. When we did prime factorization of 43126, we found that 2 x 21563 equals 43126. Since all the prime factors are unique, the square root of 43126 cannot be simplified.

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