Simplify Square Root of 67534

What is the square root of 67534 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.

√67534 = A√B

Unfortunately, the square root of 67534 cannot be simplified. Thus, here is the answer to the square root of 67534 in its simplest form:

√ 67534 = √ 67534

Here are two different methods we used to determine why the square root of 67534 cannot be simplified.

1) To be able to simplify the square root of 67534, one of the factors of 67534 other than 1 must be a perfect square. The factors of 67534 are 1, 2, 33767, and 67534. Since none of these factors are perfect squares, the square root of 67534 cannot be simplified.

2) To be able to simplify the square root of 67534, all the prime factors of 67534 cannot be unique. When we did prime factorization of 67534, we found that 2 x 33767 equals 67534. Since all the prime factors are unique, the square root of 67534 cannot be simplified.

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