Simplify Square Root of 12446

Here we will show you two methods that you can use to simplify the square root of 12446. In other words, we will show you how to find the square root of 12446 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.

√12446 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 12446 to simplify the square root of 12446. 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 12446. The factors of 12446 are 1, 2, 7, 14, 49, 98, 127, 254, 889, 1778, 6223, and 12446. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 12446 divided by the greatest perfect square from the list of all factors of 12446. We determined above that the greatest perfect square from the list of all factors of 12446 is 49. Furthermore, 12446 divided by 49 is 254, therefore B equals 254.

Now we have A and B and can get our answer to 12446 in its simplest radical form as follows:

√12446 = A√B

√12446 = 7√254

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 12446 to simplify the square root of 12446 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 12446 and then take the square root of that product. The prime factors that multiply together to make 12446 are 2 x 7 x 7 x 127. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 12446 by the number (A) squared. 7 squared is 49 and 12446 divided by 49 is 254. Therefore, B equals 254.

Once again we have A and B and can get our answer to 12446 in its simplest radical form as follows:

√12446 = A√B

√12446 = 7√254

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Simplify Square Root of 12447
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