Simplify Square Root of 10001 What is the square root of 10001 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.

10001 = A√B

Unfortunately, the square root of 10001 cannot be simplified. Thus, here is the answer to the square root of 10001 in its simplest form:

10001 = √ 10001

Here are two different methods we used to determine why the square root of 10001 cannot be simplified.

1) To be able to simplify the square root of 10001, one of the factors of 10001 other than 1 must be a perfect square. The factors of 10001 are 1, 73, 137, and 10001. Since none of these factors are perfect squares, the square root of 10001 cannot be simplified.

2) To be able to simplify the square root of 10001, all the prime factors of 10001 cannot be unique. When we did prime factorization of 10001, we found that 73 x 137 equals 10001. Since all the prime factors are unique, the square root of 10001 cannot be simplified.

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