Simplify Square Root of 38407

What is the square root of 38407 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.

√38407 = A√B

Unfortunately, the square root of 38407 cannot be simplified. Thus, here is the answer to the square root of 38407 in its simplest form:

√ 38407 = √ 38407

Here are two different methods we used to determine why the square root of 38407 cannot be simplified.

1) To be able to simplify the square root of 38407, one of the factors of 38407 other than 1 must be a perfect square. The factors of 38407 are 1, 193, 199, and 38407. Since none of these factors are perfect squares, the square root of 38407 cannot be simplified.

2) To be able to simplify the square root of 38407, all the prime factors of 38407 cannot be unique. When we did prime factorization of 38407, we found that 193 x 199 equals 38407. Since all the prime factors are unique, the square root of 38407 cannot be simplified.

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