Simplify Square Root of 34135

What is the square root of 34135 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.

√34135 = A√B

Unfortunately, the square root of 34135 cannot be simplified. Thus, here is the answer to the square root of 34135 in its simplest form:

√ 34135 = √ 34135

Here are two different methods we used to determine why the square root of 34135 cannot be simplified.

1) To be able to simplify the square root of 34135, one of the factors of 34135 other than 1 must be a perfect square. The factors of 34135 are 1, 5, 6827, and 34135. Since none of these factors are perfect squares, the square root of 34135 cannot be simplified.

2) To be able to simplify the square root of 34135, all the prime factors of 34135 cannot be unique. When we did prime factorization of 34135, we found that 5 x 6827 equals 34135. Since all the prime factors are unique, the square root of 34135 cannot be simplified.

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