Simplify Square Root of 34838

What is the square root of 34838 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.

√34838 = A√B

Unfortunately, the square root of 34838 cannot be simplified. Thus, here is the answer to the square root of 34838 in its simplest form:

√ 34838 = √ 34838

Here are two different methods we used to determine why the square root of 34838 cannot be simplified.

1) To be able to simplify the square root of 34838, one of the factors of 34838 other than 1 must be a perfect square. The factors of 34838 are 1, 2, 17419, and 34838. Since none of these factors are perfect squares, the square root of 34838 cannot be simplified.

2) To be able to simplify the square root of 34838, all the prime factors of 34838 cannot be unique. When we did prime factorization of 34838, we found that 2 x 17419 equals 34838. Since all the prime factors are unique, the square root of 34838 cannot be simplified.

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