Simplify Square Root of 1401

What is the square root of 1401 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.

√1401 = A√B

Unfortunately, the square root of 1401 cannot be simplified. Thus, here is the answer to the square root of 1401 in its simplest form:

√ 1401 = √ 1401

Here are two different methods we used to determine why the square root of 1401 cannot be simplified.

1) To be able to simplify the square root of 1401, one of the factors of 1401 other than 1 must be a perfect square. The factors of 1401 are 1, 3, 467, and 1401. Since none of these factors are perfect squares, the square root of 1401 cannot be simplified.

2) To be able to simplify the square root of 1401, all the prime factors of 1401 cannot be unique. When we did prime factorization of 1401, we found that 3 x 467 equals 1401. Since all the prime factors are unique, the square root of 1401 cannot be simplified.

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