Simplify Square Root of 36227

What is the square root of 36227 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.

√36227 = A√B

Unfortunately, the square root of 36227 cannot be simplified. Thus, here is the answer to the square root of 36227 in its simplest form:

√ 36227 = √ 36227

Here are two different methods we used to determine why the square root of 36227 cannot be simplified.

1) To be able to simplify the square root of 36227, one of the factors of 36227 other than 1 must be a perfect square. The factors of 36227 are 1, 17, 2131, and 36227. Since none of these factors are perfect squares, the square root of 36227 cannot be simplified.

2) To be able to simplify the square root of 36227, all the prime factors of 36227 cannot be unique. When we did prime factorization of 36227, we found that 17 x 2131 equals 36227. Since all the prime factors are unique, the square root of 36227 cannot be simplified.

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