Simplify Square Root of 5378

What is the square root of 5378 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.

√5378 = A√B

Unfortunately, the square root of 5378 cannot be simplified. Thus, here is the answer to the square root of 5378 in its simplest form:

√ 5378 = √ 5378

Here are two different methods we used to determine why the square root of 5378 cannot be simplified.

1) To be able to simplify the square root of 5378, one of the factors of 5378 other than 1 must be a perfect square. The factors of 5378 are 1, 2, 2689, and 5378. Since none of these factors are perfect squares, the square root of 5378 cannot be simplified.

2) To be able to simplify the square root of 5378, all the prime factors of 5378 cannot be unique. When we did prime factorization of 5378, we found that 2 x 2689 equals 5378. Since all the prime factors are unique, the square root of 5378 cannot be simplified.

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