Simplify Square Root of 3841

What is the square root of 3841 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.

√3841 = A√B

Unfortunately, the square root of 3841 cannot be simplified. Thus, here is the answer to the square root of 3841 in its simplest form:

√ 3841 = √ 3841

Here are two different methods we used to determine why the square root of 3841 cannot be simplified.

1) To be able to simplify the square root of 3841, one of the factors of 3841 other than 1 must be a perfect square. The factors of 3841 are 1, 23, 167, and 3841. Since none of these factors are perfect squares, the square root of 3841 cannot be simplified.

2) To be able to simplify the square root of 3841, all the prime factors of 3841 cannot be unique. When we did prime factorization of 3841, we found that 23 x 167 equals 3841. Since all the prime factors are unique, the square root of 3841 cannot be simplified.

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