Simplify Square Root of 19808

Here we will show you two methods that you can use to simplify the square root of 19808. In other words, we will show you how to find the square root of 19808 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.

√19808 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19808 to simplify the square root of 19808. 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 19808. The factors of 19808 are 1, 2, 4, 8, 16, 32, 619, 1238, 2476, 4952, 9904, and 19808. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 19808 divided by the greatest perfect square from the list of all factors of 19808. We determined above that the greatest perfect square from the list of all factors of 19808 is 16. Furthermore, 19808 divided by 16 is 1238, therefore B equals 1238.

Now we have A and B and can get our answer to 19808 in its simplest radical form as follows:

√19808 = A√B

√19808 = 4√1238

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19808 to simplify the square root of 19808 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 19808 and then take the square root of that product. The prime factors that multiply together to make 19808 are 2 x 2 x 2 x 2 x 2 x 619. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 19808 by the number (A) squared. 4 squared is 16 and 19808 divided by 16 is 1238. Therefore, B equals 1238.

Once again we have A and B and can get our answer to 19808 in its simplest radical form as follows:

√19808 = A√B

√19808 = 4√1238

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Simplify Square Root of 19809
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