Simplify Square Root of 23660

Here we will show you two methods that you can use to simplify the square root of 23660. In other words, we will show you how to find the square root of 23660 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.

√23660 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 23660 to simplify the square root of 23660. 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 23660. The factors of 23660 are 1, 2, 4, 5, 7, 10, 13, 14, 20, 26, 28, 35, 52, 65, 70, 91, 130, 140, 169, 182, 260, 338, 364, 455, 676, 845, 910, 1183, 1690, 1820, 2366, 3380, 4732, 5915, 11830, and 23660. Furthermore, the greatest perfect square on this list is 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Calculate 23660 divided by the greatest perfect square from the list of all factors of 23660. We determined above that the greatest perfect square from the list of all factors of 23660 is 676. Furthermore, 23660 divided by 676 is 35, therefore B equals 35.

Now we have A and B and can get our answer to 23660 in its simplest radical form as follows:

√23660 = A√B

√23660 = 26√35

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 23660 to simplify the square root of 23660 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 23660 and then take the square root of that product. The prime factors that multiply together to make 23660 are 2 x 2 x 5 x 7 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 13 x 13 = 676 and the square root of 676 is 26. Therefore, A equals 26.

B = Divide 23660 by the number (A) squared. 26 squared is 676 and 23660 divided by 676 is 35. Therefore, B equals 35.

Once again we have A and B and can get our answer to 23660 in its simplest radical form as follows:

√23660 = A√B

√23660 = 26√35

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