Simplify Square Root of 66248

Here we will show you two methods that you can use to simplify the square root of 66248. In other words, we will show you how to find the square root of 66248 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.

√66248 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 66248 to simplify the square root of 66248. 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 66248. The factors of 66248 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 49, 52, 56, 91, 98, 104, 169, 182, 196, 338, 364, 392, 637, 676, 728, 1183, 1274, 1352, 2366, 2548, 4732, 5096, 8281, 9464, 16562, 33124, and 66248. Furthermore, the greatest perfect square on this list is 33124 and the square root of 33124 is 182. Therefore, A equals 182.

B = Calculate 66248 divided by the greatest perfect square from the list of all factors of 66248. We determined above that the greatest perfect square from the list of all factors of 66248 is 33124. Furthermore, 66248 divided by 33124 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 66248 in its simplest radical form as follows:

√66248 = A√B

√66248 = 182√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 66248 to simplify the square root of 66248 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 66248 and then take the square root of that product. The prime factors that multiply together to make 66248 are 2 x 2 x 2 x 7 x 7 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 7 x 7 x 13 x 13 = 33124 and the square root of 33124 is 182. Therefore, A equals 182.

B = Divide 66248 by the number (A) squared. 182 squared is 33124 and 66248 divided by 33124 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 66248 in its simplest radical form as follows:

√66248 = A√B

√66248 = 182√2

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