Simplify Square Root of 68325

Here we will show you two methods that you can use to simplify the square root of 68325. In other words, we will show you how to find the square root of 68325 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.

√68325 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68325 to simplify the square root of 68325. 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 68325. The factors of 68325 are 1, 3, 5, 15, 25, 75, 911, 2733, 4555, 13665, 22775, and 68325. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 68325 divided by the greatest perfect square from the list of all factors of 68325. We determined above that the greatest perfect square from the list of all factors of 68325 is 25. Furthermore, 68325 divided by 25 is 2733, therefore B equals 2733.

Now we have A and B and can get our answer to 68325 in its simplest radical form as follows:

√68325 = A√B

√68325 = 5√2733

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68325 to simplify the square root of 68325 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 68325 and then take the square root of that product. The prime factors that multiply together to make 68325 are 3 x 5 x 5 x 911. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 68325 by the number (A) squared. 5 squared is 25 and 68325 divided by 25 is 2733. Therefore, B equals 2733.

Once again we have A and B and can get our answer to 68325 in its simplest radical form as follows:

√68325 = A√B

√68325 = 5√2733

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Simplify Square Root of 68326
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