Simplify Square Root of 66852

Here we will show you two methods that you can use to simplify the square root of 66852. In other words, we will show you how to find the square root of 66852 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.

√66852 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66852 to simplify the square root of 66852. 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 66852. The factors of 66852 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 619, 1238, 1857, 2476, 3714, 5571, 7428, 11142, 16713, 22284, 33426, and 66852. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 66852 divided by the greatest perfect square from the list of all factors of 66852. We determined above that the greatest perfect square from the list of all factors of 66852 is 36. Furthermore, 66852 divided by 36 is 1857, therefore B equals 1857.

Now we have A and B and can get our answer to 66852 in its simplest radical form as follows:

√66852 = A√B

√66852 = 6√1857

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66852 to simplify the square root of 66852 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 66852 and then take the square root of that product. The prime factors that multiply together to make 66852 are 2 x 2 x 3 x 3 x 3 x 619. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 66852 by the number (A) squared. 6 squared is 36 and 66852 divided by 36 is 1857. Therefore, B equals 1857.

Once again we have A and B and can get our answer to 66852 in its simplest radical form as follows:

√66852 = A√B

√66852 = 6√1857

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Simplify Square Root of 66853
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