Simplify Square Root of 5123

What is the square root of 5123 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.

√5123 = A√B

Unfortunately, the square root of 5123 cannot be simplified. Thus, here is the answer to the square root of 5123 in its simplest form:

√ 5123 = √ 5123

Here are two different methods we used to determine why the square root of 5123 cannot be simplified.

1) To be able to simplify the square root of 5123, one of the factors of 5123 other than 1 must be a perfect square. The factors of 5123 are 1, 47, 109, and 5123. Since none of these factors are perfect squares, the square root of 5123 cannot be simplified.

2) To be able to simplify the square root of 5123, all the prime factors of 5123 cannot be unique. When we did prime factorization of 5123, we found that 47 x 109 equals 5123. Since all the prime factors are unique, the square root of 5123 cannot be simplified.

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