Simplify Square Root of 397

What is the square root of 397 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.

√397 = A√B

Unfortunately, the square root of 397 cannot be simplified. Thus, here is the answer to the square root of 397 in its simplest form:

√ 397 = √ 397

Here are two different methods we used to determine why the square root of 397 cannot be simplified.

1) To be able to simplify the square root of 397, one of the factors of 397 other than 1 must be a perfect square. The factors of 397 are 1 and 397. Since none of these factors are perfect squares, the square root of 397 cannot be simplified.

2) To be able to simplify the square root of 397, all the prime factors of 397 cannot be unique. When we did prime factorization of 397, we found that 397 equals 397. Since all the prime factors are unique, the square root of 397 cannot be simplified.

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