Simplify Square Root of 51601

What is the square root of 51601 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.

√51601 = A√B

Unfortunately, the square root of 51601 cannot be simplified. Thus, here is the answer to the square root of 51601 in its simplest form:

√ 51601 = √ 51601

Here are two different methods we used to determine why the square root of 51601 cannot be simplified.

1) To be able to simplify the square root of 51601, one of the factors of 51601 other than 1 must be a perfect square. The factors of 51601 are 1, 11, 4691, and 51601. Since none of these factors are perfect squares, the square root of 51601 cannot be simplified.

2) To be able to simplify the square root of 51601, all the prime factors of 51601 cannot be unique. When we did prime factorization of 51601, we found that 11 x 4691 equals 51601. Since all the prime factors are unique, the square root of 51601 cannot be simplified.

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