Simplify Square Root of 63882

Here we will show you two methods that you can use to simplify the square root of 63882. In other words, we will show you how to find the square root of 63882 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.

√63882 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63882 to simplify the square root of 63882. 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 63882. The factors of 63882 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 54, 63, 78, 91, 117, 126, 169, 182, 189, 234, 273, 338, 351, 378, 507, 546, 702, 819, 1014, 1183, 1521, 1638, 2366, 2457, 3042, 3549, 4563, 4914, 7098, 9126, 10647, 21294, 31941, and 63882. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 63882 divided by the greatest perfect square from the list of all factors of 63882. We determined above that the greatest perfect square from the list of all factors of 63882 is 1521. Furthermore, 63882 divided by 1521 is 42, therefore B equals 42.

Now we have A and B and can get our answer to 63882 in its simplest radical form as follows:

√63882 = A√B

√63882 = 39√42

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63882 to simplify the square root of 63882 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 63882 and then take the square root of that product. The prime factors that multiply together to make 63882 are 2 x 3 x 3 x 3 x 7 x 13 x 13. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 63882 by the number (A) squared. 39 squared is 1521 and 63882 divided by 1521 is 42. Therefore, B equals 42.

Once again we have A and B and can get our answer to 63882 in its simplest radical form as follows:

√63882 = A√B

√63882 = 39√42

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