Simplify Square Root of 84640

Here we will show you two methods that you can use to simplify the square root of 84640. In other words, we will show you how to find the square root of 84640 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.

√84640 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84640 to simplify the square root of 84640. 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 84640. The factors of 84640 are 1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 529, 736, 920, 1058, 1840, 2116, 2645, 3680, 4232, 5290, 8464, 10580, 16928, 21160, 42320, and 84640. Furthermore, the greatest perfect square on this list is 8464 and the square root of 8464 is 92. Therefore, A equals 92.

B = Calculate 84640 divided by the greatest perfect square from the list of all factors of 84640. We determined above that the greatest perfect square from the list of all factors of 84640 is 8464. Furthermore, 84640 divided by 8464 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 84640 in its simplest radical form as follows:

√84640 = A√B

√84640 = 92√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84640 to simplify the square root of 84640 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 84640 and then take the square root of that product. The prime factors that multiply together to make 84640 are 2 x 2 x 2 x 2 x 2 x 5 x 23 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 23 x 23 = 8464 and the square root of 8464 is 92. Therefore, A equals 92.

B = Divide 84640 by the number (A) squared. 92 squared is 8464 and 84640 divided by 8464 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 84640 in its simplest radical form as follows:

√84640 = A√B

√84640 = 92√10

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Simplify Square Root of 84641
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