Simplify Square Root of 47338

What is the square root of 47338 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.

√47338 = A√B

Unfortunately, the square root of 47338 cannot be simplified. Thus, here is the answer to the square root of 47338 in its simplest form:

√ 47338 = √ 47338

Here are two different methods we used to determine why the square root of 47338 cannot be simplified.

1) To be able to simplify the square root of 47338, one of the factors of 47338 other than 1 must be a perfect square. The factors of 47338 are 1, 2, 23669, and 47338. Since none of these factors are perfect squares, the square root of 47338 cannot be simplified.

2) To be able to simplify the square root of 47338, all the prime factors of 47338 cannot be unique. When we did prime factorization of 47338, we found that 2 x 23669 equals 47338. Since all the prime factors are unique, the square root of 47338 cannot be simplified.

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