Simplify Square Root of 23782

What is the square root of 23782 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.

√23782 = A√B

Unfortunately, the square root of 23782 cannot be simplified. Thus, here is the answer to the square root of 23782 in its simplest form:

√ 23782 = √ 23782

Here are two different methods we used to determine why the square root of 23782 cannot be simplified.

1) To be able to simplify the square root of 23782, one of the factors of 23782 other than 1 must be a perfect square. The factors of 23782 are 1, 2, 11, 22, 23, 46, 47, 94, 253, 506, 517, 1034, 1081, 2162, 11891, and 23782. Since none of these factors are perfect squares, the square root of 23782 cannot be simplified.

2) To be able to simplify the square root of 23782, all the prime factors of 23782 cannot be unique. When we did prime factorization of 23782, we found that 2 x 11 x 23 x 47 equals 23782. Since all the prime factors are unique, the square root of 23782 cannot be simplified.

Simplify Square Root
Please enter another square root in the box below for us to simplify for you.

Simplify Square Root of 23783
Here is the next square root on our list that we have simplifed.