Simplify Square Root of 1753

What is the square root of 1753 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.

√1753 = A√B

Unfortunately, the square root of 1753 cannot be simplified. Thus, here is the answer to the square root of 1753 in its simplest form:

√ 1753 = √ 1753

Here are two different methods we used to determine why the square root of 1753 cannot be simplified.

1) To be able to simplify the square root of 1753, one of the factors of 1753 other than 1 must be a perfect square. The factors of 1753 are 1 and 1753. Since none of these factors are perfect squares, the square root of 1753 cannot be simplified.

2) To be able to simplify the square root of 1753, all the prime factors of 1753 cannot be unique. When we did prime factorization of 1753, we found that 1753 equals 1753. Since all the prime factors are unique, the square root of 1753 cannot be simplified.

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