Simplify Square Root of 46245

What is the square root of 46245 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.

√46245 = A√B

Unfortunately, the square root of 46245 cannot be simplified. Thus, here is the answer to the square root of 46245 in its simplest form:

√ 46245 = √ 46245

Here are two different methods we used to determine why the square root of 46245 cannot be simplified.

1) To be able to simplify the square root of 46245, one of the factors of 46245 other than 1 must be a perfect square. The factors of 46245 are 1, 3, 5, 15, 3083, 9249, 15415, and 46245. Since none of these factors are perfect squares, the square root of 46245 cannot be simplified.

2) To be able to simplify the square root of 46245, all the prime factors of 46245 cannot be unique. When we did prime factorization of 46245, we found that 3 x 5 x 3083 equals 46245. Since all the prime factors are unique, the square root of 46245 cannot be simplified.

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