Simplify Square Root of 1723

What is the square root of 1723 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.

√1723 = A√B

Unfortunately, the square root of 1723 cannot be simplified. Thus, here is the answer to the square root of 1723 in its simplest form:

√ 1723 = √ 1723

Here are two different methods we used to determine why the square root of 1723 cannot be simplified.

1) To be able to simplify the square root of 1723, one of the factors of 1723 other than 1 must be a perfect square. The factors of 1723 are 1 and 1723. Since none of these factors are perfect squares, the square root of 1723 cannot be simplified.

2) To be able to simplify the square root of 1723, all the prime factors of 1723 cannot be unique. When we did prime factorization of 1723, we found that 1723 equals 1723. Since all the prime factors are unique, the square root of 1723 cannot be simplified.

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