Simplify Square Root of 87009

What is the square root of 87009 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.

√87009 = A√B

Unfortunately, the square root of 87009 cannot be simplified. Thus, here is the answer to the square root of 87009 in its simplest form:

√ 87009 = √ 87009

Here are two different methods we used to determine why the square root of 87009 cannot be simplified.

1) To be able to simplify the square root of 87009, one of the factors of 87009 other than 1 must be a perfect square. The factors of 87009 are 1, 3, 13, 23, 39, 69, 97, 291, 299, 897, 1261, 2231, 3783, 6693, 29003, and 87009. Since none of these factors are perfect squares, the square root of 87009 cannot be simplified.

2) To be able to simplify the square root of 87009, all the prime factors of 87009 cannot be unique. When we did prime factorization of 87009, we found that 3 x 13 x 23 x 97 equals 87009. Since all the prime factors are unique, the square root of 87009 cannot be simplified.

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