Simplify Square Root of 48959

What is the square root of 48959 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.

√48959 = A√B

Unfortunately, the square root of 48959 cannot be simplified. Thus, here is the answer to the square root of 48959 in its simplest form:

√ 48959 = √ 48959

Here are two different methods we used to determine why the square root of 48959 cannot be simplified.

1) To be able to simplify the square root of 48959, one of the factors of 48959 other than 1 must be a perfect square. The factors of 48959 are 1, 173, 283, and 48959. Since none of these factors are perfect squares, the square root of 48959 cannot be simplified.

2) To be able to simplify the square root of 48959, all the prime factors of 48959 cannot be unique. When we did prime factorization of 48959, we found that 173 x 283 equals 48959. Since all the prime factors are unique, the square root of 48959 cannot be simplified.

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