Simplify Square Root of 46803

What is the square root of 46803 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.

√46803 = A√B

Unfortunately, the square root of 46803 cannot be simplified. Thus, here is the answer to the square root of 46803 in its simplest form:

√ 46803 = √ 46803

Here are two different methods we used to determine why the square root of 46803 cannot be simplified.

1) To be able to simplify the square root of 46803, one of the factors of 46803 other than 1 must be a perfect square. The factors of 46803 are 1, 3, 15601, and 46803. Since none of these factors are perfect squares, the square root of 46803 cannot be simplified.

2) To be able to simplify the square root of 46803, all the prime factors of 46803 cannot be unique. When we did prime factorization of 46803, we found that 3 x 15601 equals 46803. Since all the prime factors are unique, the square root of 46803 cannot be simplified.

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