Simplify Square Root of 46778

What is the square root of 46778 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.

√46778 = A√B

Unfortunately, the square root of 46778 cannot be simplified. Thus, here is the answer to the square root of 46778 in its simplest form:

√ 46778 = √ 46778

Here are two different methods we used to determine why the square root of 46778 cannot be simplified.

1) To be able to simplify the square root of 46778, one of the factors of 46778 other than 1 must be a perfect square. The factors of 46778 are 1, 2, 19, 38, 1231, 2462, 23389, and 46778. Since none of these factors are perfect squares, the square root of 46778 cannot be simplified.

2) To be able to simplify the square root of 46778, all the prime factors of 46778 cannot be unique. When we did prime factorization of 46778, we found that 2 x 19 x 1231 equals 46778. Since all the prime factors are unique, the square root of 46778 cannot be simplified.

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