Simplify Square Root of 19663

Here we will show you two methods that you can use to simplify the square root of 19663. In other words, we will show you how to find the square root of 19663 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.

√19663 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19663 to simplify the square root of 19663. 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 19663. The factors of 19663 are 1, 7, 53, 371, 2809, and 19663. Furthermore, the greatest perfect square on this list is 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Calculate 19663 divided by the greatest perfect square from the list of all factors of 19663. We determined above that the greatest perfect square from the list of all factors of 19663 is 2809. Furthermore, 19663 divided by 2809 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 19663 in its simplest radical form as follows:

√19663 = A√B

√19663 = 53√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19663 to simplify the square root of 19663 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 19663 and then take the square root of that product. The prime factors that multiply together to make 19663 are 7 x 53 x 53. When we strip out the pairs only, we get 53 x 53 = 2809 and the square root of 2809 is 53. Therefore, A equals 53.

B = Divide 19663 by the number (A) squared. 53 squared is 2809 and 19663 divided by 2809 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 19663 in its simplest radical form as follows:

√19663 = A√B

√19663 = 53√7

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Simplify Square Root of 19664
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