Simplify Square Root of 21203

What is the square root of 21203 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.

√21203 = A√B

Unfortunately, the square root of 21203 cannot be simplified. Thus, here is the answer to the square root of 21203 in its simplest form:

√ 21203 = √ 21203

Here are two different methods we used to determine why the square root of 21203 cannot be simplified.

1) To be able to simplify the square root of 21203, one of the factors of 21203 other than 1 must be a perfect square. The factors of 21203 are 1, 7, 13, 91, 233, 1631, 3029, and 21203. Since none of these factors are perfect squares, the square root of 21203 cannot be simplified.

2) To be able to simplify the square root of 21203, all the prime factors of 21203 cannot be unique. When we did prime factorization of 21203, we found that 7 x 13 x 233 equals 21203. Since all the prime factors are unique, the square root of 21203 cannot be simplified.

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