Simplify Square Root of 11305

What is the square root of 11305 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.

√11305 = A√B

Unfortunately, the square root of 11305 cannot be simplified. Thus, here is the answer to the square root of 11305 in its simplest form:

√ 11305 = √ 11305

Here are two different methods we used to determine why the square root of 11305 cannot be simplified.

1) To be able to simplify the square root of 11305, one of the factors of 11305 other than 1 must be a perfect square. The factors of 11305 are 1, 5, 7, 17, 19, 35, 85, 95, 119, 133, 323, 595, 665, 1615, 2261, and 11305. Since none of these factors are perfect squares, the square root of 11305 cannot be simplified.

2) To be able to simplify the square root of 11305, all the prime factors of 11305 cannot be unique. When we did prime factorization of 11305, we found that 5 x 7 x 17 x 19 equals 11305. Since all the prime factors are unique, the square root of 11305 cannot be simplified.

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