Simplify Square Root of 51101

What is the square root of 51101 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.

√51101 = A√B

Unfortunately, the square root of 51101 cannot be simplified. Thus, here is the answer to the square root of 51101 in its simplest form:

√ 51101 = √ 51101

Here are two different methods we used to determine why the square root of 51101 cannot be simplified.

1) To be able to simplify the square root of 51101, one of the factors of 51101 other than 1 must be a perfect square. The factors of 51101 are 1, 137, 373, and 51101. Since none of these factors are perfect squares, the square root of 51101 cannot be simplified.

2) To be able to simplify the square root of 51101, all the prime factors of 51101 cannot be unique. When we did prime factorization of 51101, we found that 137 x 373 equals 51101. Since all the prime factors are unique, the square root of 51101 cannot be simplified.

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