Simplify Square Root of 75061

What is the square root of 75061 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.

√75061 = A√B

Unfortunately, the square root of 75061 cannot be simplified. Thus, here is the answer to the square root of 75061 in its simplest form:

√ 75061 = √ 75061

Here are two different methods we used to determine why the square root of 75061 cannot be simplified.

1) To be able to simplify the square root of 75061, one of the factors of 75061 other than 1 must be a perfect square. The factors of 75061 are 1, 7, 10723, and 75061. Since none of these factors are perfect squares, the square root of 75061 cannot be simplified.

2) To be able to simplify the square root of 75061, all the prime factors of 75061 cannot be unique. When we did prime factorization of 75061, we found that 7 x 10723 equals 75061. Since all the prime factors are unique, the square root of 75061 cannot be simplified.

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