Simplify Square Root of 23505

What is the square root of 23505 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.

√23505 = A√B

Unfortunately, the square root of 23505 cannot be simplified. Thus, here is the answer to the square root of 23505 in its simplest form:

√ 23505 = √ 23505

Here are two different methods we used to determine why the square root of 23505 cannot be simplified.

1) To be able to simplify the square root of 23505, one of the factors of 23505 other than 1 must be a perfect square. The factors of 23505 are 1, 3, 5, 15, 1567, 4701, 7835, and 23505. Since none of these factors are perfect squares, the square root of 23505 cannot be simplified.

2) To be able to simplify the square root of 23505, all the prime factors of 23505 cannot be unique. When we did prime factorization of 23505, we found that 3 x 5 x 1567 equals 23505. Since all the prime factors are unique, the square root of 23505 cannot be simplified.

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