Simplify Square Root of 8430

What is the square root of 8430 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.

√8430 = A√B

Unfortunately, the square root of 8430 cannot be simplified. Thus, here is the answer to the square root of 8430 in its simplest form:

√ 8430 = √ 8430

Here are two different methods we used to determine why the square root of 8430 cannot be simplified.

1) To be able to simplify the square root of 8430, one of the factors of 8430 other than 1 must be a perfect square. The factors of 8430 are 1, 2, 3, 5, 6, 10, 15, 30, 281, 562, 843, 1405, 1686, 2810, 4215, and 8430. Since none of these factors are perfect squares, the square root of 8430 cannot be simplified.

2) To be able to simplify the square root of 8430, all the prime factors of 8430 cannot be unique. When we did prime factorization of 8430, we found that 2 x 3 x 5 x 281 equals 8430. Since all the prime factors are unique, the square root of 8430 cannot be simplified.

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