Simplify Square Root of 69897

What is the square root of 69897 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.

√69897 = A√B

Unfortunately, the square root of 69897 cannot be simplified. Thus, here is the answer to the square root of 69897 in its simplest form:

√ 69897 = √ 69897

Here are two different methods we used to determine why the square root of 69897 cannot be simplified.

1) To be able to simplify the square root of 69897, one of the factors of 69897 other than 1 must be a perfect square. The factors of 69897 are 1, 3, 23, 69, 1013, 3039, 23299, and 69897. Since none of these factors are perfect squares, the square root of 69897 cannot be simplified.

2) To be able to simplify the square root of 69897, all the prime factors of 69897 cannot be unique. When we did prime factorization of 69897, we found that 3 x 23 x 1013 equals 69897. Since all the prime factors are unique, the square root of 69897 cannot be simplified.

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