Simplify Square Root of 6123

What is the square root of 6123 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.

√6123 = A√B

Unfortunately, the square root of 6123 cannot be simplified. Thus, here is the answer to the square root of 6123 in its simplest form:

√ 6123 = √ 6123

Here are two different methods we used to determine why the square root of 6123 cannot be simplified.

1) To be able to simplify the square root of 6123, one of the factors of 6123 other than 1 must be a perfect square. The factors of 6123 are 1, 3, 13, 39, 157, 471, 2041, and 6123. Since none of these factors are perfect squares, the square root of 6123 cannot be simplified.

2) To be able to simplify the square root of 6123, all the prime factors of 6123 cannot be unique. When we did prime factorization of 6123, we found that 3 x 13 x 157 equals 6123. Since all the prime factors are unique, the square root of 6123 cannot be simplified.

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