Simplify Square Root of 5293

What is the square root of 5293 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.

√5293 = A√B

Unfortunately, the square root of 5293 cannot be simplified. Thus, here is the answer to the square root of 5293 in its simplest form:

√ 5293 = √ 5293

Here are two different methods we used to determine why the square root of 5293 cannot be simplified.

1) To be able to simplify the square root of 5293, one of the factors of 5293 other than 1 must be a perfect square. The factors of 5293 are 1, 67, 79, and 5293. Since none of these factors are perfect squares, the square root of 5293 cannot be simplified.

2) To be able to simplify the square root of 5293, all the prime factors of 5293 cannot be unique. When we did prime factorization of 5293, we found that 67 x 79 equals 5293. Since all the prime factors are unique, the square root of 5293 cannot be simplified.

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