Simplify Square Root of 45393

What is the square root of 45393 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.

√45393 = A√B

Unfortunately, the square root of 45393 cannot be simplified. Thus, here is the answer to the square root of 45393 in its simplest form:

√ 45393 = √ 45393

Here are two different methods we used to determine why the square root of 45393 cannot be simplified.

1) To be able to simplify the square root of 45393, one of the factors of 45393 other than 1 must be a perfect square. The factors of 45393 are 1, 3, 15131, and 45393. Since none of these factors are perfect squares, the square root of 45393 cannot be simplified.

2) To be able to simplify the square root of 45393, all the prime factors of 45393 cannot be unique. When we did prime factorization of 45393, we found that 3 x 15131 equals 45393. Since all the prime factors are unique, the square root of 45393 cannot be simplified.

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