Simplify Square Root of 53633

What is the square root of 53633 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.

√53633 = A√B

Unfortunately, the square root of 53633 cannot be simplified. Thus, here is the answer to the square root of 53633 in its simplest form:

√ 53633 = √ 53633

Here are two different methods we used to determine why the square root of 53633 cannot be simplified.

1) To be able to simplify the square root of 53633, one of the factors of 53633 other than 1 must be a perfect square. The factors of 53633 are 1 and 53633. Since none of these factors are perfect squares, the square root of 53633 cannot be simplified.

2) To be able to simplify the square root of 53633, all the prime factors of 53633 cannot be unique. When we did prime factorization of 53633, we found that 53633 equals 53633. Since all the prime factors are unique, the square root of 53633 cannot be simplified.

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