Simplify Square Root of 61762

What is the square root of 61762 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.

√61762 = A√B

Unfortunately, the square root of 61762 cannot be simplified. Thus, here is the answer to the square root of 61762 in its simplest form:

√ 61762 = √ 61762

Here are two different methods we used to determine why the square root of 61762 cannot be simplified.

1) To be able to simplify the square root of 61762, one of the factors of 61762 other than 1 must be a perfect square. The factors of 61762 are 1, 2, 30881, and 61762. Since none of these factors are perfect squares, the square root of 61762 cannot be simplified.

2) To be able to simplify the square root of 61762, all the prime factors of 61762 cannot be unique. When we did prime factorization of 61762, we found that 2 x 30881 equals 61762. Since all the prime factors are unique, the square root of 61762 cannot be simplified.

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