Simplify Square Root of 45363

What is the square root of 45363 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.

√45363 = A√B

Unfortunately, the square root of 45363 cannot be simplified. Thus, here is the answer to the square root of 45363 in its simplest form:

√ 45363 = √ 45363

Here are two different methods we used to determine why the square root of 45363 cannot be simplified.

1) To be able to simplify the square root of 45363, one of the factors of 45363 other than 1 must be a perfect square. The factors of 45363 are 1, 3, 15121, and 45363. Since none of these factors are perfect squares, the square root of 45363 cannot be simplified.

2) To be able to simplify the square root of 45363, all the prime factors of 45363 cannot be unique. When we did prime factorization of 45363, we found that 3 x 15121 equals 45363. Since all the prime factors are unique, the square root of 45363 cannot be simplified.

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