Simplify Square Root of 32469

What is the square root of 32469 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.

√32469 = A√B

Unfortunately, the square root of 32469 cannot be simplified. Thus, here is the answer to the square root of 32469 in its simplest form:

√ 32469 = √ 32469

Here are two different methods we used to determine why the square root of 32469 cannot be simplified.

1) To be able to simplify the square root of 32469, one of the factors of 32469 other than 1 must be a perfect square. The factors of 32469 are 1, 3, 79, 137, 237, 411, 10823, and 32469. Since none of these factors are perfect squares, the square root of 32469 cannot be simplified.

2) To be able to simplify the square root of 32469, all the prime factors of 32469 cannot be unique. When we did prime factorization of 32469, we found that 3 x 79 x 137 equals 32469. Since all the prime factors are unique, the square root of 32469 cannot be simplified.

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