Simplify Square Root of 68770

Here we will show you two methods that you can use to simplify the square root of 68770. In other words, we will show you how to find the square root of 68770 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.

√68770 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68770 to simplify the square root of 68770. 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 68770. The factors of 68770 are 1, 2, 5, 10, 13, 23, 26, 46, 65, 115, 130, 230, 299, 529, 598, 1058, 1495, 2645, 2990, 5290, 6877, 13754, 34385, and 68770. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 68770 divided by the greatest perfect square from the list of all factors of 68770. We determined above that the greatest perfect square from the list of all factors of 68770 is 529. Furthermore, 68770 divided by 529 is 130, therefore B equals 130.

Now we have A and B and can get our answer to 68770 in its simplest radical form as follows:

√68770 = A√B

√68770 = 23√130

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68770 to simplify the square root of 68770 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 68770 and then take the square root of that product. The prime factors that multiply together to make 68770 are 2 x 5 x 13 x 23 x 23. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 68770 by the number (A) squared. 23 squared is 529 and 68770 divided by 529 is 130. Therefore, B equals 130.

Once again we have A and B and can get our answer to 68770 in its simplest radical form as follows:

√68770 = A√B

√68770 = 23√130

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Simplify Square Root of 68771
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