Simplify Square Root of 11238

What is the square root of 11238 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.

√11238 = A√B

Unfortunately, the square root of 11238 cannot be simplified. Thus, here is the answer to the square root of 11238 in its simplest form:

√ 11238 = √ 11238

Here are two different methods we used to determine why the square root of 11238 cannot be simplified.

1) To be able to simplify the square root of 11238, one of the factors of 11238 other than 1 must be a perfect square. The factors of 11238 are 1, 2, 3, 6, 1873, 3746, 5619, and 11238. Since none of these factors are perfect squares, the square root of 11238 cannot be simplified.

2) To be able to simplify the square root of 11238, all the prime factors of 11238 cannot be unique. When we did prime factorization of 11238, we found that 2 x 3 x 1873 equals 11238. Since all the prime factors are unique, the square root of 11238 cannot be simplified.

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