Simplify Square Root of 84512

Here we will show you two methods that you can use to simplify the square root of 84512. In other words, we will show you how to find the square root of 84512 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.

√84512 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84512 to simplify the square root of 84512. 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 84512. The factors of 84512 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 139, 152, 278, 304, 556, 608, 1112, 2224, 2641, 4448, 5282, 10564, 21128, 42256, and 84512. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 84512 divided by the greatest perfect square from the list of all factors of 84512. We determined above that the greatest perfect square from the list of all factors of 84512 is 16. Furthermore, 84512 divided by 16 is 5282, therefore B equals 5282.

Now we have A and B and can get our answer to 84512 in its simplest radical form as follows:

√84512 = A√B

√84512 = 4√5282

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84512 to simplify the square root of 84512 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 84512 and then take the square root of that product. The prime factors that multiply together to make 84512 are 2 x 2 x 2 x 2 x 2 x 19 x 139. 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 84512 by the number (A) squared. 4 squared is 16 and 84512 divided by 16 is 5282. Therefore, B equals 5282.

Once again we have A and B and can get our answer to 84512 in its simplest radical form as follows:

√84512 = A√B

√84512 = 4√5282

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