Simplify Square Root of 10594

What is the square root of 10594 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.

√10594 = A√B

Unfortunately, the square root of 10594 cannot be simplified. Thus, here is the answer to the square root of 10594 in its simplest form:

√ 10594 = √ 10594

Here are two different methods we used to determine why the square root of 10594 cannot be simplified.

1) To be able to simplify the square root of 10594, one of the factors of 10594 other than 1 must be a perfect square. The factors of 10594 are 1, 2, 5297, and 10594. Since none of these factors are perfect squares, the square root of 10594 cannot be simplified.

2) To be able to simplify the square root of 10594, all the prime factors of 10594 cannot be unique. When we did prime factorization of 10594, we found that 2 x 5297 equals 10594. Since all the prime factors are unique, the square root of 10594 cannot be simplified.

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