Simplify Square Root of 463

What is the square root of 463 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.

√463 = A√B

Unfortunately, the square root of 463 cannot be simplified. Thus, here is the answer to the square root of 463 in its simplest form:

√ 463 = √ 463

Here are two different methods we used to determine why the square root of 463 cannot be simplified.

1) To be able to simplify the square root of 463, one of the factors of 463 other than 1 must be a perfect square. The factors of 463 are 1 and 463. Since none of these factors are perfect squares, the square root of 463 cannot be simplified.

2) To be able to simplify the square root of 463, all the prime factors of 463 cannot be unique. When we did prime factorization of 463, we found that 463 equals 463. Since all the prime factors are unique, the square root of 463 cannot be simplified.

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