Simplify Square Root of 77333

What is the square root of 77333 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.

√77333 = A√B

Unfortunately, the square root of 77333 cannot be simplified. Thus, here is the answer to the square root of 77333 in its simplest form:

√ 77333 = √ 77333

Here are two different methods we used to determine why the square root of 77333 cannot be simplified.

1) To be able to simplify the square root of 77333, one of the factors of 77333 other than 1 must be a perfect square. The factors of 77333 are 1, 17, 4549, and 77333. Since none of these factors are perfect squares, the square root of 77333 cannot be simplified.

2) To be able to simplify the square root of 77333, all the prime factors of 77333 cannot be unique. When we did prime factorization of 77333, we found that 17 x 4549 equals 77333. Since all the prime factors are unique, the square root of 77333 cannot be simplified.

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