Simplify Square Root of 84080

Here we will show you two methods that you can use to simplify the square root of 84080. In other words, we will show you how to find the square root of 84080 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.

√84080 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84080 to simplify the square root of 84080. 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 84080. The factors of 84080 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 1051, 2102, 4204, 5255, 8408, 10510, 16816, 21020, 42040, and 84080. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 84080 divided by the greatest perfect square from the list of all factors of 84080. We determined above that the greatest perfect square from the list of all factors of 84080 is 16. Furthermore, 84080 divided by 16 is 5255, therefore B equals 5255.

Now we have A and B and can get our answer to 84080 in its simplest radical form as follows:

√84080 = A√B

√84080 = 4√5255

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84080 to simplify the square root of 84080 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 84080 and then take the square root of that product. The prime factors that multiply together to make 84080 are 2 x 2 x 2 x 2 x 5 x 1051. 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 84080 by the number (A) squared. 4 squared is 16 and 84080 divided by 16 is 5255. Therefore, B equals 5255.

Once again we have A and B and can get our answer to 84080 in its simplest radical form as follows:

√84080 = A√B

√84080 = 4√5255

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Simplify Square Root of 84081
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