Simplify Square Root of 47222

What is the square root of 47222 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.

√47222 = A√B

Unfortunately, the square root of 47222 cannot be simplified. Thus, here is the answer to the square root of 47222 in its simplest form:

√ 47222 = √ 47222

Here are two different methods we used to determine why the square root of 47222 cannot be simplified.

1) To be able to simplify the square root of 47222, one of the factors of 47222 other than 1 must be a perfect square. The factors of 47222 are 1, 2, 7, 14, 3373, 6746, 23611, and 47222. Since none of these factors are perfect squares, the square root of 47222 cannot be simplified.

2) To be able to simplify the square root of 47222, all the prime factors of 47222 cannot be unique. When we did prime factorization of 47222, we found that 2 x 7 x 3373 equals 47222. Since all the prime factors are unique, the square root of 47222 cannot be simplified.

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