Simplify Square Root of 80106

Here we will show you two methods that you can use to simplify the square root of 80106. In other words, we will show you how to find the square root of 80106 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.

√80106 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80106 to simplify the square root of 80106. 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 80106. The factors of 80106 are 1, 2, 3, 6, 13, 26, 39, 78, 79, 158, 169, 237, 338, 474, 507, 1014, 1027, 2054, 3081, 6162, 13351, 26702, 40053, and 80106. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 80106 divided by the greatest perfect square from the list of all factors of 80106. We determined above that the greatest perfect square from the list of all factors of 80106 is 169. Furthermore, 80106 divided by 169 is 474, therefore B equals 474.

Now we have A and B and can get our answer to 80106 in its simplest radical form as follows:

√80106 = A√B

√80106 = 13√474

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80106 to simplify the square root of 80106 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 80106 and then take the square root of that product. The prime factors that multiply together to make 80106 are 2 x 3 x 13 x 13 x 79. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 80106 by the number (A) squared. 13 squared is 169 and 80106 divided by 169 is 474. Therefore, B equals 474.

Once again we have A and B and can get our answer to 80106 in its simplest radical form as follows:

√80106 = A√B

√80106 = 13√474

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Simplify Square Root of 80107
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