Simplify Square Root of 15203

What is the square root of 15203 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.

√15203 = A√B

Unfortunately, the square root of 15203 cannot be simplified. Thus, here is the answer to the square root of 15203 in its simplest form:

√ 15203 = √ 15203

Here are two different methods we used to determine why the square root of 15203 cannot be simplified.

1) To be able to simplify the square root of 15203, one of the factors of 15203 other than 1 must be a perfect square. The factors of 15203 are 1, 23, 661, and 15203. Since none of these factors are perfect squares, the square root of 15203 cannot be simplified.

2) To be able to simplify the square root of 15203, all the prime factors of 15203 cannot be unique. When we did prime factorization of 15203, we found that 23 x 661 equals 15203. Since all the prime factors are unique, the square root of 15203 cannot be simplified.

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