Simplify Square Root of 53798

What is the square root of 53798 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.

√53798 = A√B

Unfortunately, the square root of 53798 cannot be simplified. Thus, here is the answer to the square root of 53798 in its simplest form:

√ 53798 = √ 53798

Here are two different methods we used to determine why the square root of 53798 cannot be simplified.

1) To be able to simplify the square root of 53798, one of the factors of 53798 other than 1 must be a perfect square. The factors of 53798 are 1, 2, 37, 74, 727, 1454, 26899, and 53798. Since none of these factors are perfect squares, the square root of 53798 cannot be simplified.

2) To be able to simplify the square root of 53798, all the prime factors of 53798 cannot be unique. When we did prime factorization of 53798, we found that 2 x 37 x 727 equals 53798. Since all the prime factors are unique, the square root of 53798 cannot be simplified.

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