Simplify Square Root of 67154

What is the square root of 67154 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.

√67154 = A√B

Unfortunately, the square root of 67154 cannot be simplified. Thus, here is the answer to the square root of 67154 in its simplest form:

√ 67154 = √ 67154

Here are two different methods we used to determine why the square root of 67154 cannot be simplified.

1) To be able to simplify the square root of 67154, one of the factors of 67154 other than 1 must be a perfect square. The factors of 67154 are 1, 2, 33577, and 67154. Since none of these factors are perfect squares, the square root of 67154 cannot be simplified.

2) To be able to simplify the square root of 67154, all the prime factors of 67154 cannot be unique. When we did prime factorization of 67154, we found that 2 x 33577 equals 67154. Since all the prime factors are unique, the square root of 67154 cannot be simplified.

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