Simplify Square Root of 19476

Here we will show you two methods that you can use to simplify the square root of 19476. In other words, we will show you how to find the square root of 19476 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.

√19476 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19476 to simplify the square root of 19476. 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 19476. The factors of 19476 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 541, 1082, 1623, 2164, 3246, 4869, 6492, 9738, and 19476. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 19476 divided by the greatest perfect square from the list of all factors of 19476. We determined above that the greatest perfect square from the list of all factors of 19476 is 36. Furthermore, 19476 divided by 36 is 541, therefore B equals 541.

Now we have A and B and can get our answer to 19476 in its simplest radical form as follows:

√19476 = A√B

√19476 = 6√541

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19476 to simplify the square root of 19476 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 19476 and then take the square root of that product. The prime factors that multiply together to make 19476 are 2 x 2 x 3 x 3 x 541. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 19476 by the number (A) squared. 6 squared is 36 and 19476 divided by 36 is 541. Therefore, B equals 541.

Once again we have A and B and can get our answer to 19476 in its simplest radical form as follows:

√19476 = A√B

√19476 = 6√541

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 19477
Here is the next square root on our list that we have simplifed for you.