Simplify Square Root of 75407

What is the square root of 75407 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.

√75407 = A√B

Unfortunately, the square root of 75407 cannot be simplified. Thus, here is the answer to the square root of 75407 in its simplest form:

√ 75407 = √ 75407

Here are two different methods we used to determine why the square root of 75407 cannot be simplified.

1) To be able to simplify the square root of 75407, one of the factors of 75407 other than 1 must be a perfect square. The factors of 75407 are 1 and 75407. Since none of these factors are perfect squares, the square root of 75407 cannot be simplified.

2) To be able to simplify the square root of 75407, all the prime factors of 75407 cannot be unique. When we did prime factorization of 75407, we found that 75407 equals 75407. Since all the prime factors are unique, the square root of 75407 cannot be simplified.

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