Simplify Square Root of 45907

What is the square root of 45907 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.

√45907 = A√B

Unfortunately, the square root of 45907 cannot be simplified. Thus, here is the answer to the square root of 45907 in its simplest form:

√ 45907 = √ 45907

Here are two different methods we used to determine why the square root of 45907 cannot be simplified.

1) To be able to simplify the square root of 45907, one of the factors of 45907 other than 1 must be a perfect square. The factors of 45907 are 1, 29, 1583, and 45907. Since none of these factors are perfect squares, the square root of 45907 cannot be simplified.

2) To be able to simplify the square root of 45907, all the prime factors of 45907 cannot be unique. When we did prime factorization of 45907, we found that 29 x 1583 equals 45907. Since all the prime factors are unique, the square root of 45907 cannot be simplified.

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