Simplify Square Root of 17305

What is the square root of 17305 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.

√17305 = A√B

Unfortunately, the square root of 17305 cannot be simplified. Thus, here is the answer to the square root of 17305 in its simplest form:

√ 17305 = √ 17305

Here are two different methods we used to determine why the square root of 17305 cannot be simplified.

1) To be able to simplify the square root of 17305, one of the factors of 17305 other than 1 must be a perfect square. The factors of 17305 are 1, 5, 3461, and 17305. Since none of these factors are perfect squares, the square root of 17305 cannot be simplified.

2) To be able to simplify the square root of 17305, all the prime factors of 17305 cannot be unique. When we did prime factorization of 17305, we found that 5 x 3461 equals 17305. Since all the prime factors are unique, the square root of 17305 cannot be simplified.

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