Simplify Square Root of 473

What is the square root of 473 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.

√473 = A√B

Unfortunately, the square root of 473 cannot be simplified. Thus, here is the answer to the square root of 473 in its simplest form:

√ 473 = √ 473

Here are two different methods we used to determine why the square root of 473 cannot be simplified.

1) To be able to simplify the square root of 473, one of the factors of 473 other than 1 must be a perfect square. The factors of 473 are 1, 11, 43, and 473. Since none of these factors are perfect squares, the square root of 473 cannot be simplified.

2) To be able to simplify the square root of 473, all the prime factors of 473 cannot be unique. When we did prime factorization of 473, we found that 11 x 43 equals 473. Since all the prime factors are unique, the square root of 473 cannot be simplified.

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