Simplify Square Root of 13184

Here we will show you two methods that you can use to simplify the square root of 13184. In other words, we will show you how to find the square root of 13184 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.

√13184 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 13184 to simplify the square root of 13184. 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 13184. The factors of 13184 are 1, 2, 4, 8, 16, 32, 64, 103, 128, 206, 412, 824, 1648, 3296, 6592, and 13184. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 13184 divided by the greatest perfect square from the list of all factors of 13184. We determined above that the greatest perfect square from the list of all factors of 13184 is 64. Furthermore, 13184 divided by 64 is 206, therefore B equals 206.

Now we have A and B and can get our answer to 13184 in its simplest radical form as follows:

√13184 = A√B

√13184 = 8√206

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 13184 to simplify the square root of 13184 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 13184 and then take the square root of that product. The prime factors that multiply together to make 13184 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 103. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 13184 by the number (A) squared. 8 squared is 64 and 13184 divided by 64 is 206. Therefore, B equals 206.

Once again we have A and B and can get our answer to 13184 in its simplest radical form as follows:

√13184 = A√B

√13184 = 8√206

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Simplify Square Root of 13185
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