Simplify Square Root of 8065

What is the square root of 8065 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.

√8065 = A√B

Unfortunately, the square root of 8065 cannot be simplified. Thus, here is the answer to the square root of 8065 in its simplest form:

√ 8065 = √ 8065

Here are two different methods we used to determine why the square root of 8065 cannot be simplified.

1) To be able to simplify the square root of 8065, one of the factors of 8065 other than 1 must be a perfect square. The factors of 8065 are 1, 5, 1613, and 8065. Since none of these factors are perfect squares, the square root of 8065 cannot be simplified.

2) To be able to simplify the square root of 8065, all the prime factors of 8065 cannot be unique. When we did prime factorization of 8065, we found that 5 x 1613 equals 8065. Since all the prime factors are unique, the square root of 8065 cannot be simplified.

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