Simplify Square Root of 45295

What is the square root of 45295 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.

√45295 = A√B

Unfortunately, the square root of 45295 cannot be simplified. Thus, here is the answer to the square root of 45295 in its simplest form:

√ 45295 = √ 45295

Here are two different methods we used to determine why the square root of 45295 cannot be simplified.

1) To be able to simplify the square root of 45295, one of the factors of 45295 other than 1 must be a perfect square. The factors of 45295 are 1, 5, 9059, and 45295. Since none of these factors are perfect squares, the square root of 45295 cannot be simplified.

2) To be able to simplify the square root of 45295, all the prime factors of 45295 cannot be unique. When we did prime factorization of 45295, we found that 5 x 9059 equals 45295. Since all the prime factors are unique, the square root of 45295 cannot be simplified.

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