Simplify Square Root of 42802

What is the square root of 42802 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.

√42802 = A√B

Unfortunately, the square root of 42802 cannot be simplified. Thus, here is the answer to the square root of 42802 in its simplest form:

√ 42802 = √ 42802

Here are two different methods we used to determine why the square root of 42802 cannot be simplified.

1) To be able to simplify the square root of 42802, one of the factors of 42802 other than 1 must be a perfect square. The factors of 42802 are 1, 2, 21401, and 42802. Since none of these factors are perfect squares, the square root of 42802 cannot be simplified.

2) To be able to simplify the square root of 42802, all the prime factors of 42802 cannot be unique. When we did prime factorization of 42802, we found that 2 x 21401 equals 42802. Since all the prime factors are unique, the square root of 42802 cannot be simplified.

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