Simplify Square Root of 45933

What is the square root of 45933 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.

√45933 = A√B

Unfortunately, the square root of 45933 cannot be simplified. Thus, here is the answer to the square root of 45933 in its simplest form:

√ 45933 = √ 45933

Here are two different methods we used to determine why the square root of 45933 cannot be simplified.

1) To be able to simplify the square root of 45933, one of the factors of 45933 other than 1 must be a perfect square. The factors of 45933 are 1, 3, 61, 183, 251, 753, 15311, and 45933. Since none of these factors are perfect squares, the square root of 45933 cannot be simplified.

2) To be able to simplify the square root of 45933, all the prime factors of 45933 cannot be unique. When we did prime factorization of 45933, we found that 3 x 61 x 251 equals 45933. Since all the prime factors are unique, the square root of 45933 cannot be simplified.

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