Simplify Square Root of 30

What is the square root of 30 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.

√30 = A√B

Unfortunately, the square root of 30 cannot be simplified. Thus, here is the answer to the square root of 30 in its simplest form:

√ 30 = √ 30

Here are two different methods we used to determine why the square root of 30 cannot be simplified.

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

2) To be able to simplify the square root of 30, all the prime factors of 30 cannot be unique. When we did prime factorization of 30, we found that 2 x 3 x 5 equals 30. Since all the prime factors are unique, the square root of 30 cannot be simplified.

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