Simplify Square Root of 50905

What is the square root of 50905 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.

√50905 = A√B

Unfortunately, the square root of 50905 cannot be simplified. Thus, here is the answer to the square root of 50905 in its simplest form:

√ 50905 = √ 50905

Here are two different methods we used to determine why the square root of 50905 cannot be simplified.

1) To be able to simplify the square root of 50905, one of the factors of 50905 other than 1 must be a perfect square. The factors of 50905 are 1, 5, 10181, and 50905. Since none of these factors are perfect squares, the square root of 50905 cannot be simplified.

2) To be able to simplify the square root of 50905, all the prime factors of 50905 cannot be unique. When we did prime factorization of 50905, we found that 5 x 10181 equals 50905. Since all the prime factors are unique, the square root of 50905 cannot be simplified.

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