Simplify Square Root of 12423

What is the square root of 12423 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.

√12423 = A√B

Unfortunately, the square root of 12423 cannot be simplified. Thus, here is the answer to the square root of 12423 in its simplest form:

√ 12423 = √ 12423

Here are two different methods we used to determine why the square root of 12423 cannot be simplified.

1) To be able to simplify the square root of 12423, one of the factors of 12423 other than 1 must be a perfect square. The factors of 12423 are 1, 3, 41, 101, 123, 303, 4141, and 12423. Since none of these factors are perfect squares, the square root of 12423 cannot be simplified.

2) To be able to simplify the square root of 12423, all the prime factors of 12423 cannot be unique. When we did prime factorization of 12423, we found that 3 x 41 x 101 equals 12423. Since all the prime factors are unique, the square root of 12423 cannot be simplified.

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