Simplify Square Root of 68003

What is the square root of 68003 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.

√68003 = A√B

Unfortunately, the square root of 68003 cannot be simplified. Thus, here is the answer to the square root of 68003 in its simplest form:

√ 68003 = √ 68003

Here are two different methods we used to determine why the square root of 68003 cannot be simplified.

1) To be able to simplify the square root of 68003, one of the factors of 68003 other than 1 must be a perfect square. The factors of 68003 are 1, 13, 5231, and 68003. Since none of these factors are perfect squares, the square root of 68003 cannot be simplified.

2) To be able to simplify the square root of 68003, all the prime factors of 68003 cannot be unique. When we did prime factorization of 68003, we found that 13 x 5231 equals 68003. Since all the prime factors are unique, the square root of 68003 cannot be simplified.

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