Simplify Square Root of 19304

Here we will show you two methods that you can use to simplify the square root of 19304. In other words, we will show you how to find the square root of 19304 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.

√19304 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19304 to simplify the square root of 19304. 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 19304. The factors of 19304 are 1, 2, 4, 8, 19, 38, 76, 127, 152, 254, 508, 1016, 2413, 4826, 9652, and 19304. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 19304 divided by the greatest perfect square from the list of all factors of 19304. We determined above that the greatest perfect square from the list of all factors of 19304 is 4. Furthermore, 19304 divided by 4 is 4826, therefore B equals 4826.

Now we have A and B and can get our answer to 19304 in its simplest radical form as follows:

√19304 = A√B

√19304 = 2√4826

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19304 to simplify the square root of 19304 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 19304 and then take the square root of that product. The prime factors that multiply together to make 19304 are 2 x 2 x 2 x 19 x 127. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 19304 by the number (A) squared. 2 squared is 4 and 19304 divided by 4 is 4826. Therefore, B equals 4826.

Once again we have A and B and can get our answer to 19304 in its simplest radical form as follows:

√19304 = A√B

√19304 = 2√4826

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