Simplify Square Root of 45817

What is the square root of 45817 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.

√45817 = A√B

Unfortunately, the square root of 45817 cannot be simplified. Thus, here is the answer to the square root of 45817 in its simplest form:

√ 45817 = √ 45817

Here are two different methods we used to determine why the square root of 45817 cannot be simplified.

1) To be able to simplify the square root of 45817, one of the factors of 45817 other than 1 must be a perfect square. The factors of 45817 are 1 and 45817. Since none of these factors are perfect squares, the square root of 45817 cannot be simplified.

2) To be able to simplify the square root of 45817, all the prime factors of 45817 cannot be unique. When we did prime factorization of 45817, we found that 45817 equals 45817. Since all the prime factors are unique, the square root of 45817 cannot be simplified.

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