Simplify Square Root of 81456

Here we will show you two methods that you can use to simplify the square root of 81456. In other words, we will show you how to find the square root of 81456 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.

√81456 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81456 to simplify the square root of 81456. 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 81456. The factors of 81456 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1697, 3394, 5091, 6788, 10182, 13576, 20364, 27152, 40728, and 81456. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 81456 divided by the greatest perfect square from the list of all factors of 81456. We determined above that the greatest perfect square from the list of all factors of 81456 is 16. Furthermore, 81456 divided by 16 is 5091, therefore B equals 5091.

Now we have A and B and can get our answer to 81456 in its simplest radical form as follows:

√81456 = A√B

√81456 = 4√5091

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81456 to simplify the square root of 81456 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 81456 and then take the square root of that product. The prime factors that multiply together to make 81456 are 2 x 2 x 2 x 2 x 3 x 1697. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 81456 by the number (A) squared. 4 squared is 16 and 81456 divided by 16 is 5091. Therefore, B equals 5091.

Once again we have A and B and can get our answer to 81456 in its simplest radical form as follows:

√81456 = A√B

√81456 = 4√5091

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Simplify Square Root of 81457
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