Simplify Square Root of 13448

Here we will show you two methods that you can use to simplify the square root of 13448. In other words, we will show you how to find the square root of 13448 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.

√13448 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 13448 to simplify the square root of 13448. 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 13448. The factors of 13448 are 1, 2, 4, 8, 41, 82, 164, 328, 1681, 3362, 6724, and 13448. Furthermore, the greatest perfect square on this list is 6724 and the square root of 6724 is 82. Therefore, A equals 82.

B = Calculate 13448 divided by the greatest perfect square from the list of all factors of 13448. We determined above that the greatest perfect square from the list of all factors of 13448 is 6724. Furthermore, 13448 divided by 6724 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 13448 in its simplest radical form as follows:

√13448 = A√B

√13448 = 82√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 13448 to simplify the square root of 13448 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 13448 and then take the square root of that product. The prime factors that multiply together to make 13448 are 2 x 2 x 2 x 41 x 41. When we strip out the pairs only, we get 2 x 2 x 41 x 41 = 6724 and the square root of 6724 is 82. Therefore, A equals 82.

B = Divide 13448 by the number (A) squared. 82 squared is 6724 and 13448 divided by 6724 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 13448 in its simplest radical form as follows:

√13448 = A√B

√13448 = 82√2

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Simplify Square Root of 13449
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