Simplify Square Root of 57681

Here we will show you two methods that you can use to simplify the square root of 57681. In other words, we will show you how to find the square root of 57681 in its simplest radical form using two different methods.

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.

√57681 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57681 to simplify the square root of 57681. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 57681. The factors of 57681 are 1, 3, 9, 13, 17, 29, 39, 51, 87, 117, 153, 221, 261, 377, 493, 663, 1131, 1479, 1989, 3393, 4437, 6409, 19227, and 57681. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 57681 divided by the greatest perfect square from the list of all factors of 57681. We determined above that the greatest perfect square from the list of all factors of 57681 is 9. Furthermore, 57681 divided by 9 is 6409, therefore B equals 6409.

Now we have A and B and can get our answer to 57681 in its simplest radical form as follows:

√57681 = A√B

√57681 = 3√6409

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57681 to simplify the square root of 57681 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 57681 and then take the square root of that product. The prime factors that multiply together to make 57681 are 3 x 3 x 13 x 17 x 29. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 57681 by the number (A) squared. 3 squared is 9 and 57681 divided by 9 is 6409. Therefore, B equals 6409.

Once again we have A and B and can get our answer to 57681 in its simplest radical form as follows:

√57681 = A√B

√57681 = 3√6409

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Simplify Square Root of 57682
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