Simplify Square Root of 14993

What is the square root of 14993 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.

√14993 = A√B

Unfortunately, the square root of 14993 cannot be simplified. Thus, here is the answer to the square root of 14993 in its simplest form:

√ 14993 = √ 14993

Here are two different methods we used to determine why the square root of 14993 cannot be simplified.

1) To be able to simplify the square root of 14993, one of the factors of 14993 other than 1 must be a perfect square. The factors of 14993 are 1, 11, 29, 47, 319, 517, 1363, and 14993. Since none of these factors are perfect squares, the square root of 14993 cannot be simplified.

2) To be able to simplify the square root of 14993, all the prime factors of 14993 cannot be unique. When we did prime factorization of 14993, we found that 11 x 29 x 47 equals 14993. Since all the prime factors are unique, the square root of 14993 cannot be simplified.

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