Simplify Square Root of 68100

Here we will show you two methods that you can use to simplify the square root of 68100. In other words, we will show you how to find the square root of 68100 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.

√68100 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68100 to simplify the square root of 68100. 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 68100. The factors of 68100 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 227, 300, 454, 681, 908, 1135, 1362, 2270, 2724, 3405, 4540, 5675, 6810, 11350, 13620, 17025, 22700, 34050, and 68100. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 68100 divided by the greatest perfect square from the list of all factors of 68100. We determined above that the greatest perfect square from the list of all factors of 68100 is 100. Furthermore, 68100 divided by 100 is 681, therefore B equals 681.

Now we have A and B and can get our answer to 68100 in its simplest radical form as follows:

√68100 = A√B

√68100 = 10√681

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68100 to simplify the square root of 68100 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 68100 and then take the square root of that product. The prime factors that multiply together to make 68100 are 2 x 2 x 3 x 5 x 5 x 227. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 68100 by the number (A) squared. 10 squared is 100 and 68100 divided by 100 is 681. Therefore, B equals 681.

Once again we have A and B and can get our answer to 68100 in its simplest radical form as follows:

√68100 = A√B

√68100 = 10√681

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