Simplify Square Root of 64762

What is the square root of 64762 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.

√64762 = A√B

Unfortunately, the square root of 64762 cannot be simplified. Thus, here is the answer to the square root of 64762 in its simplest form:

√ 64762 = √ 64762

Here are two different methods we used to determine why the square root of 64762 cannot be simplified.

1) To be able to simplify the square root of 64762, one of the factors of 64762 other than 1 must be a perfect square. The factors of 64762 are 1, 2, 32381, and 64762. Since none of these factors are perfect squares, the square root of 64762 cannot be simplified.

2) To be able to simplify the square root of 64762, all the prime factors of 64762 cannot be unique. When we did prime factorization of 64762, we found that 2 x 32381 equals 64762. Since all the prime factors are unique, the square root of 64762 cannot be simplified.

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