Simplify Square Root of 67267

What is the square root of 67267 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.

√67267 = A√B

Unfortunately, the square root of 67267 cannot be simplified. Thus, here is the answer to the square root of 67267 in its simplest form:

√ 67267 = √ 67267

Here are two different methods we used to determine why the square root of 67267 cannot be simplified.

1) To be able to simplify the square root of 67267, one of the factors of 67267 other than 1 must be a perfect square. The factors of 67267 are 1, 137, 491, and 67267. Since none of these factors are perfect squares, the square root of 67267 cannot be simplified.

2) To be able to simplify the square root of 67267, all the prime factors of 67267 cannot be unique. When we did prime factorization of 67267, we found that 137 x 491 equals 67267. Since all the prime factors are unique, the square root of 67267 cannot be simplified.

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