Simplify Square Root of 42665

What is the square root of 42665 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.

√42665 = A√B

Unfortunately, the square root of 42665 cannot be simplified. Thus, here is the answer to the square root of 42665 in its simplest form:

√ 42665 = √ 42665

Here are two different methods we used to determine why the square root of 42665 cannot be simplified.

1) To be able to simplify the square root of 42665, one of the factors of 42665 other than 1 must be a perfect square. The factors of 42665 are 1, 5, 7, 23, 35, 53, 115, 161, 265, 371, 805, 1219, 1855, 6095, 8533, and 42665. Since none of these factors are perfect squares, the square root of 42665 cannot be simplified.

2) To be able to simplify the square root of 42665, all the prime factors of 42665 cannot be unique. When we did prime factorization of 42665, we found that 5 x 7 x 23 x 53 equals 42665. Since all the prime factors are unique, the square root of 42665 cannot be simplified.

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