Simplify Square Root of 35538

What is the square root of 35538 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.

√35538 = A√B

Unfortunately, the square root of 35538 cannot be simplified. Thus, here is the answer to the square root of 35538 in its simplest form:

√ 35538 = √ 35538

Here are two different methods we used to determine why the square root of 35538 cannot be simplified.

1) To be able to simplify the square root of 35538, one of the factors of 35538 other than 1 must be a perfect square. The factors of 35538 are 1, 2, 3, 6, 5923, 11846, 17769, and 35538. Since none of these factors are perfect squares, the square root of 35538 cannot be simplified.

2) To be able to simplify the square root of 35538, all the prime factors of 35538 cannot be unique. When we did prime factorization of 35538, we found that 2 x 3 x 5923 equals 35538. Since all the prime factors are unique, the square root of 35538 cannot be simplified.

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