Simplify Square Root of 47




What is the square root of 47 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.

47 = A√B

Unfortunately, the square root of 47 cannot be simplified. Thus, here is the answer to the square root of 47 in its simplest form:

47 = √ 47


Here are two different methods we used to determine why the square root of 47 cannot be simplified.

1) To be able to simplify the square root of 47, one of the factors of 47 other than 1 must be a perfect square. The factors of 47 are 1 and 47. Since none of these factors are perfect squares, the square root of 47 cannot be simplified.

2) To be able to simplify the square root of 47, all the prime factors of 47 cannot be unique. When we did prime factorization of 47, we found that 47 equals 47. Since all the prime factors are unique, the square root of 47 cannot be simplified.



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