Simplify Square Root of 23295

What is the square root of 23295 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.

√23295 = A√B

Unfortunately, the square root of 23295 cannot be simplified. Thus, here is the answer to the square root of 23295 in its simplest form:

√ 23295 = √ 23295

Here are two different methods we used to determine why the square root of 23295 cannot be simplified.

1) To be able to simplify the square root of 23295, one of the factors of 23295 other than 1 must be a perfect square. The factors of 23295 are 1, 3, 5, 15, 1553, 4659, 7765, and 23295. Since none of these factors are perfect squares, the square root of 23295 cannot be simplified.

2) To be able to simplify the square root of 23295, all the prime factors of 23295 cannot be unique. When we did prime factorization of 23295, we found that 3 x 5 x 1553 equals 23295. Since all the prime factors are unique, the square root of 23295 cannot be simplified.

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