Simplify Square Root of 34561

What is the square root of 34561 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.

√34561 = A√B

Unfortunately, the square root of 34561 cannot be simplified. Thus, here is the answer to the square root of 34561 in its simplest form:

√ 34561 = √ 34561

Here are two different methods we used to determine why the square root of 34561 cannot be simplified.

1) To be able to simplify the square root of 34561, one of the factors of 34561 other than 1 must be a perfect square. The factors of 34561 are 1, 17, 19, 107, 323, 1819, 2033, and 34561. Since none of these factors are perfect squares, the square root of 34561 cannot be simplified.

2) To be able to simplify the square root of 34561, all the prime factors of 34561 cannot be unique. When we did prime factorization of 34561, we found that 17 x 19 x 107 equals 34561. Since all the prime factors are unique, the square root of 34561 cannot be simplified.

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