Simplify Square Root of 48783

What is the square root of 48783 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.

√48783 = A√B

Unfortunately, the square root of 48783 cannot be simplified. Thus, here is the answer to the square root of 48783 in its simplest form:

√ 48783 = √ 48783

Here are two different methods we used to determine why the square root of 48783 cannot be simplified.

1) To be able to simplify the square root of 48783, one of the factors of 48783 other than 1 must be a perfect square. The factors of 48783 are 1, 3, 7, 21, 23, 69, 101, 161, 303, 483, 707, 2121, 2323, 6969, 16261, and 48783. Since none of these factors are perfect squares, the square root of 48783 cannot be simplified.

2) To be able to simplify the square root of 48783, all the prime factors of 48783 cannot be unique. When we did prime factorization of 48783, we found that 3 x 7 x 23 x 101 equals 48783. Since all the prime factors are unique, the square root of 48783 cannot be simplified.

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