Simplify Square Root of 12349

What is the square root of 12349 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.

√12349 = A√B

Unfortunately, the square root of 12349 cannot be simplified. Thus, here is the answer to the square root of 12349 in its simplest form:

√ 12349 = √ 12349

Here are two different methods we used to determine why the square root of 12349 cannot be simplified.

1) To be able to simplify the square root of 12349, one of the factors of 12349 other than 1 must be a perfect square. The factors of 12349 are 1, 53, 233, and 12349. Since none of these factors are perfect squares, the square root of 12349 cannot be simplified.

2) To be able to simplify the square root of 12349, all the prime factors of 12349 cannot be unique. When we did prime factorization of 12349, we found that 53 x 233 equals 12349. Since all the prime factors are unique, the square root of 12349 cannot be simplified.

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