Simplify Square Root of 12448

Here we will show you two methods that you can use to simplify the square root of 12448. In other words, we will show you how to find the square root of 12448 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.

√12448 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12448 to simplify the square root of 12448. 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 12448. The factors of 12448 are 1, 2, 4, 8, 16, 32, 389, 778, 1556, 3112, 6224, and 12448. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 12448 divided by the greatest perfect square from the list of all factors of 12448. We determined above that the greatest perfect square from the list of all factors of 12448 is 16. Furthermore, 12448 divided by 16 is 778, therefore B equals 778.

Now we have A and B and can get our answer to 12448 in its simplest radical form as follows:

√12448 = A√B

√12448 = 4√778

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12448 to simplify the square root of 12448 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 12448 and then take the square root of that product. The prime factors that multiply together to make 12448 are 2 x 2 x 2 x 2 x 2 x 389. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 12448 by the number (A) squared. 4 squared is 16 and 12448 divided by 16 is 778. Therefore, B equals 778.

Once again we have A and B and can get our answer to 12448 in its simplest radical form as follows:

√12448 = A√B

√12448 = 4√778

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Simplify Square Root of 12449
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