Simplify Square Root of 68357

What is the square root of 68357 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.

√68357 = A√B

Unfortunately, the square root of 68357 cannot be simplified. Thus, here is the answer to the square root of 68357 in its simplest form:

√ 68357 = √ 68357

Here are two different methods we used to determine why the square root of 68357 cannot be simplified.

1) To be able to simplify the square root of 68357, one of the factors of 68357 other than 1 must be a perfect square. The factors of 68357 are 1, 17, 4021, and 68357. Since none of these factors are perfect squares, the square root of 68357 cannot be simplified.

2) To be able to simplify the square root of 68357, all the prime factors of 68357 cannot be unique. When we did prime factorization of 68357, we found that 17 x 4021 equals 68357. Since all the prime factors are unique, the square root of 68357 cannot be simplified.

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