Simplify Square Root of 12416

Here we will show you two methods that you can use to simplify the square root of 12416. In other words, we will show you how to find the square root of 12416 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.

√12416 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12416 to simplify the square root of 12416. 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 12416. The factors of 12416 are 1, 2, 4, 8, 16, 32, 64, 97, 128, 194, 388, 776, 1552, 3104, 6208, and 12416. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 12416 divided by the greatest perfect square from the list of all factors of 12416. We determined above that the greatest perfect square from the list of all factors of 12416 is 64. Furthermore, 12416 divided by 64 is 194, therefore B equals 194.

Now we have A and B and can get our answer to 12416 in its simplest radical form as follows:

√12416 = A√B

√12416 = 8√194

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12416 to simplify the square root of 12416 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 12416 and then take the square root of that product. The prime factors that multiply together to make 12416 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 97. 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 12416 by the number (A) squared. 8 squared is 64 and 12416 divided by 64 is 194. Therefore, B equals 194.

Once again we have A and B and can get our answer to 12416 in its simplest radical form as follows:

√12416 = A√B

√12416 = 8√194

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Simplify Square Root of 12417
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