Simplify Square Root of 81412

Here we will show you two methods that you can use to simplify the square root of 81412. In other words, we will show you how to find the square root of 81412 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.

√81412 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81412 to simplify the square root of 81412. 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 81412. The factors of 81412 are 1, 2, 4, 20353, 40706, and 81412. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 81412 divided by the greatest perfect square from the list of all factors of 81412. We determined above that the greatest perfect square from the list of all factors of 81412 is 4. Furthermore, 81412 divided by 4 is 20353, therefore B equals 20353.

Now we have A and B and can get our answer to 81412 in its simplest radical form as follows:

√81412 = A√B

√81412 = 2√20353

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81412 to simplify the square root of 81412 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 81412 and then take the square root of that product. The prime factors that multiply together to make 81412 are 2 x 2 x 20353. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 81412 by the number (A) squared. 2 squared is 4 and 81412 divided by 4 is 20353. Therefore, B equals 20353.

Once again we have A and B and can get our answer to 81412 in its simplest radical form as follows:

√81412 = A√B

√81412 = 2√20353

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Simplify Square Root of 81413
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