Simplify Square Root of 33527

What is the square root of 33527 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.

√33527 = A√B

Unfortunately, the square root of 33527 cannot be simplified. Thus, here is the answer to the square root of 33527 in its simplest form:

√ 33527 = √ 33527

Here are two different methods we used to determine why the square root of 33527 cannot be simplified.

1) To be able to simplify the square root of 33527, one of the factors of 33527 other than 1 must be a perfect square. The factors of 33527 are 1, 13, 2579, and 33527. Since none of these factors are perfect squares, the square root of 33527 cannot be simplified.

2) To be able to simplify the square root of 33527, all the prime factors of 33527 cannot be unique. When we did prime factorization of 33527, we found that 13 x 2579 equals 33527. Since all the prime factors are unique, the square root of 33527 cannot be simplified.

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