Simplify Square Root of 5754

What is the square root of 5754 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.

√5754 = A√B

Unfortunately, the square root of 5754 cannot be simplified. Thus, here is the answer to the square root of 5754 in its simplest form:

√ 5754 = √ 5754

Here are two different methods we used to determine why the square root of 5754 cannot be simplified.

1) To be able to simplify the square root of 5754, one of the factors of 5754 other than 1 must be a perfect square. The factors of 5754 are 1, 2, 3, 6, 7, 14, 21, 42, 137, 274, 411, 822, 959, 1918, 2877, and 5754. Since none of these factors are perfect squares, the square root of 5754 cannot be simplified.

2) To be able to simplify the square root of 5754, all the prime factors of 5754 cannot be unique. When we did prime factorization of 5754, we found that 2 x 3 x 7 x 137 equals 5754. Since all the prime factors are unique, the square root of 5754 cannot be simplified.

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