Simplify Square Root of 10640

Here we will show you two methods that you can use to simplify the square root of 10640. In other words, we will show you how to find the square root of 10640 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.

√10640 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10640 to simplify the square root of 10640. 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 10640. The factors of 10640 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 19, 20, 28, 35, 38, 40, 56, 70, 76, 80, 95, 112, 133, 140, 152, 190, 266, 280, 304, 380, 532, 560, 665, 760, 1064, 1330, 1520, 2128, 2660, 5320, and 10640. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 10640 divided by the greatest perfect square from the list of all factors of 10640. We determined above that the greatest perfect square from the list of all factors of 10640 is 16. Furthermore, 10640 divided by 16 is 665, therefore B equals 665.

Now we have A and B and can get our answer to 10640 in its simplest radical form as follows:

√10640 = A√B

√10640 = 4√665

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10640 to simplify the square root of 10640 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 10640 and then take the square root of that product. The prime factors that multiply together to make 10640 are 2 x 2 x 2 x 2 x 5 x 7 x 19. 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 10640 by the number (A) squared. 4 squared is 16 and 10640 divided by 16 is 665. Therefore, B equals 665.

Once again we have A and B and can get our answer to 10640 in its simplest radical form as follows:

√10640 = A√B

√10640 = 4√665

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