Simplify Square Root of 23649

What is the square root of 23649 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.

√23649 = A√B

Unfortunately, the square root of 23649 cannot be simplified. Thus, here is the answer to the square root of 23649 in its simplest form:

√ 23649 = √ 23649

Here are two different methods we used to determine why the square root of 23649 cannot be simplified.

1) To be able to simplify the square root of 23649, one of the factors of 23649 other than 1 must be a perfect square. The factors of 23649 are 1, 3, 7883, and 23649. Since none of these factors are perfect squares, the square root of 23649 cannot be simplified.

2) To be able to simplify the square root of 23649, all the prime factors of 23649 cannot be unique. When we did prime factorization of 23649, we found that 3 x 7883 equals 23649. Since all the prime factors are unique, the square root of 23649 cannot be simplified.

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