Simplify Square Root of 67485

What is the square root of 67485 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.

√67485 = A√B

Unfortunately, the square root of 67485 cannot be simplified. Thus, here is the answer to the square root of 67485 in its simplest form:

√ 67485 = √ 67485

Here are two different methods we used to determine why the square root of 67485 cannot be simplified.

1) To be able to simplify the square root of 67485, one of the factors of 67485 other than 1 must be a perfect square. The factors of 67485 are 1, 3, 5, 11, 15, 33, 55, 165, 409, 1227, 2045, 4499, 6135, 13497, 22495, and 67485. Since none of these factors are perfect squares, the square root of 67485 cannot be simplified.

2) To be able to simplify the square root of 67485, all the prime factors of 67485 cannot be unique. When we did prime factorization of 67485, we found that 3 x 5 x 11 x 409 equals 67485. Since all the prime factors are unique, the square root of 67485 cannot be simplified.

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