Simplify Square Root of 36827

What is the square root of 36827 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.

√36827 = A√B

Unfortunately, the square root of 36827 cannot be simplified. Thus, here is the answer to the square root of 36827 in its simplest form:

√ 36827 = √ 36827

Here are two different methods we used to determine why the square root of 36827 cannot be simplified.

1) To be able to simplify the square root of 36827, one of the factors of 36827 other than 1 must be a perfect square. The factors of 36827 are 1, 7, 5261, and 36827. Since none of these factors are perfect squares, the square root of 36827 cannot be simplified.

2) To be able to simplify the square root of 36827, all the prime factors of 36827 cannot be unique. When we did prime factorization of 36827, we found that 7 x 5261 equals 36827. Since all the prime factors are unique, the square root of 36827 cannot be simplified.

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