Simplify Square Root of 11582

What is the square root of 11582 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.

√11582 = A√B

Unfortunately, the square root of 11582 cannot be simplified. Thus, here is the answer to the square root of 11582 in its simplest form:

√ 11582 = √ 11582

Here are two different methods we used to determine why the square root of 11582 cannot be simplified.

1) To be able to simplify the square root of 11582, one of the factors of 11582 other than 1 must be a perfect square. The factors of 11582 are 1, 2, 5791, and 11582. Since none of these factors are perfect squares, the square root of 11582 cannot be simplified.

2) To be able to simplify the square root of 11582, all the prime factors of 11582 cannot be unique. When we did prime factorization of 11582, we found that 2 x 5791 equals 11582. Since all the prime factors are unique, the square root of 11582 cannot be simplified.

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