Simplify Square Root of 51478

What is the square root of 51478 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.

√51478 = A√B

Unfortunately, the square root of 51478 cannot be simplified. Thus, here is the answer to the square root of 51478 in its simplest form:

√ 51478 = √ 51478

Here are two different methods we used to determine why the square root of 51478 cannot be simplified.

1) To be able to simplify the square root of 51478, one of the factors of 51478 other than 1 must be a perfect square. The factors of 51478 are 1, 2, 7, 14, 3677, 7354, 25739, and 51478. Since none of these factors are perfect squares, the square root of 51478 cannot be simplified.

2) To be able to simplify the square root of 51478, all the prime factors of 51478 cannot be unique. When we did prime factorization of 51478, we found that 2 x 7 x 3677 equals 51478. Since all the prime factors are unique, the square root of 51478 cannot be simplified.

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