Simplify Square Root of 36219

What is the square root of 36219 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.

√36219 = A√B

Unfortunately, the square root of 36219 cannot be simplified. Thus, here is the answer to the square root of 36219 in its simplest form:

√ 36219 = √ 36219

Here are two different methods we used to determine why the square root of 36219 cannot be simplified.

1) To be able to simplify the square root of 36219, one of the factors of 36219 other than 1 must be a perfect square. The factors of 36219 are 1, 3, 12073, and 36219. Since none of these factors are perfect squares, the square root of 36219 cannot be simplified.

2) To be able to simplify the square root of 36219, all the prime factors of 36219 cannot be unique. When we did prime factorization of 36219, we found that 3 x 12073 equals 36219. Since all the prime factors are unique, the square root of 36219 cannot be simplified.

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