Simplify Square Root of 19456

Here we will show you two methods that you can use to simplify the square root of 19456. In other words, we will show you how to find the square root of 19456 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.

√19456 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19456 to simplify the square root of 19456. 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 19456. The factors of 19456 are 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1024, 1216, 2432, 4864, 9728, and 19456. Furthermore, the greatest perfect square on this list is 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Calculate 19456 divided by the greatest perfect square from the list of all factors of 19456. We determined above that the greatest perfect square from the list of all factors of 19456 is 1024. Furthermore, 19456 divided by 1024 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 19456 in its simplest radical form as follows:

√19456 = A√B

√19456 = 32√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19456 to simplify the square root of 19456 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 19456 and then take the square root of that product. The prime factors that multiply together to make 19456 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 19. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Divide 19456 by the number (A) squared. 32 squared is 1024 and 19456 divided by 1024 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 19456 in its simplest radical form as follows:

√19456 = A√B

√19456 = 32√19

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