Simplify Square Root of 33205

What is the square root of 33205 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.

√33205 = A√B

Unfortunately, the square root of 33205 cannot be simplified. Thus, here is the answer to the square root of 33205 in its simplest form:

√ 33205 = √ 33205

Here are two different methods we used to determine why the square root of 33205 cannot be simplified.

1) To be able to simplify the square root of 33205, one of the factors of 33205 other than 1 must be a perfect square. The factors of 33205 are 1, 5, 29, 145, 229, 1145, 6641, and 33205. Since none of these factors are perfect squares, the square root of 33205 cannot be simplified.

2) To be able to simplify the square root of 33205, all the prime factors of 33205 cannot be unique. When we did prime factorization of 33205, we found that 5 x 29 x 229 equals 33205. Since all the prime factors are unique, the square root of 33205 cannot be simplified.

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