Simplify Square Root of 50629

What is the square root of 50629 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.

√50629 = A√B

Unfortunately, the square root of 50629 cannot be simplified. Thus, here is the answer to the square root of 50629 in its simplest form:

√ 50629 = √ 50629

Here are two different methods we used to determine why the square root of 50629 cannot be simplified.

1) To be able to simplify the square root of 50629, one of the factors of 50629 other than 1 must be a perfect square. The factors of 50629 are 1, 197, 257, and 50629. Since none of these factors are perfect squares, the square root of 50629 cannot be simplified.

2) To be able to simplify the square root of 50629, all the prime factors of 50629 cannot be unique. When we did prime factorization of 50629, we found that 197 x 257 equals 50629. Since all the prime factors are unique, the square root of 50629 cannot be simplified.

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