Simplify Square Root of 68528

Here we will show you two methods that you can use to simplify the square root of 68528. In other words, we will show you how to find the square root of 68528 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.

√68528 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68528 to simplify the square root of 68528. 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 68528. The factors of 68528 are 1, 2, 4, 8, 16, 4283, 8566, 17132, 34264, and 68528. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 68528 divided by the greatest perfect square from the list of all factors of 68528. We determined above that the greatest perfect square from the list of all factors of 68528 is 16. Furthermore, 68528 divided by 16 is 4283, therefore B equals 4283.

Now we have A and B and can get our answer to 68528 in its simplest radical form as follows:

√68528 = A√B

√68528 = 4√4283

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68528 to simplify the square root of 68528 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 68528 and then take the square root of that product. The prime factors that multiply together to make 68528 are 2 x 2 x 2 x 2 x 4283. 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 68528 by the number (A) squared. 4 squared is 16 and 68528 divided by 16 is 4283. Therefore, B equals 4283.

Once again we have A and B and can get our answer to 68528 in its simplest radical form as follows:

√68528 = A√B

√68528 = 4√4283

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Simplify Square Root of 68529
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