Simplify Square Root of 84162

Here we will show you two methods that you can use to simplify the square root of 84162. In other words, we will show you how to find the square root of 84162 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.

√84162 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84162 to simplify the square root of 84162. 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 84162. The factors of 84162 are 1, 2, 3, 6, 13, 26, 39, 78, 83, 166, 169, 249, 338, 498, 507, 1014, 1079, 2158, 3237, 6474, 14027, 28054, 42081, and 84162. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 84162 divided by the greatest perfect square from the list of all factors of 84162. We determined above that the greatest perfect square from the list of all factors of 84162 is 169. Furthermore, 84162 divided by 169 is 498, therefore B equals 498.

Now we have A and B and can get our answer to 84162 in its simplest radical form as follows:

√84162 = A√B

√84162 = 13√498

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84162 to simplify the square root of 84162 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 84162 and then take the square root of that product. The prime factors that multiply together to make 84162 are 2 x 3 x 13 x 13 x 83. 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 84162 by the number (A) squared. 13 squared is 169 and 84162 divided by 169 is 498. Therefore, B equals 498.

Once again we have A and B and can get our answer to 84162 in its simplest radical form as follows:

√84162 = A√B

√84162 = 13√498

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Simplify Square Root of 84163
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