Simplify Square Root of 14735

What is the square root of 14735 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.

√14735 = A√B

Unfortunately, the square root of 14735 cannot be simplified. Thus, here is the answer to the square root of 14735 in its simplest form:

√ 14735 = √ 14735

Here are two different methods we used to determine why the square root of 14735 cannot be simplified.

1) To be able to simplify the square root of 14735, one of the factors of 14735 other than 1 must be a perfect square. The factors of 14735 are 1, 5, 7, 35, 421, 2105, 2947, and 14735. Since none of these factors are perfect squares, the square root of 14735 cannot be simplified.

2) To be able to simplify the square root of 14735, all the prime factors of 14735 cannot be unique. When we did prime factorization of 14735, we found that 5 x 7 x 421 equals 14735. Since all the prime factors are unique, the square root of 14735 cannot be simplified.

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