Simplify Square Root of 81608

Here we will show you two methods that you can use to simplify the square root of 81608. In other words, we will show you how to find the square root of 81608 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.

√81608 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81608 to simplify the square root of 81608. 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 81608. The factors of 81608 are 1, 2, 4, 8, 101, 202, 404, 808, 10201, 20402, 40804, and 81608. Furthermore, the greatest perfect square on this list is 40804 and the square root of 40804 is 202. Therefore, A equals 202.

B = Calculate 81608 divided by the greatest perfect square from the list of all factors of 81608. We determined above that the greatest perfect square from the list of all factors of 81608 is 40804. Furthermore, 81608 divided by 40804 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 81608 in its simplest radical form as follows:

√81608 = A√B

√81608 = 202√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81608 to simplify the square root of 81608 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 81608 and then take the square root of that product. The prime factors that multiply together to make 81608 are 2 x 2 x 2 x 101 x 101. When we strip out the pairs only, we get 2 x 2 x 101 x 101 = 40804 and the square root of 40804 is 202. Therefore, A equals 202.

B = Divide 81608 by the number (A) squared. 202 squared is 40804 and 81608 divided by 40804 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 81608 in its simplest radical form as follows:

√81608 = A√B

√81608 = 202√2

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Simplify Square Root of 81609
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