Simplify Square Root of 19773

Here we will show you two methods that you can use to simplify the square root of 19773. In other words, we will show you how to find the square root of 19773 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.

√19773 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19773 to simplify the square root of 19773. 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 19773. The factors of 19773 are 1, 3, 9, 13, 39, 117, 169, 507, 1521, 2197, 6591, and 19773. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 19773 divided by the greatest perfect square from the list of all factors of 19773. We determined above that the greatest perfect square from the list of all factors of 19773 is 1521. Furthermore, 19773 divided by 1521 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 19773 in its simplest radical form as follows:

√19773 = A√B

√19773 = 39√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19773 to simplify the square root of 19773 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 19773 and then take the square root of that product. The prime factors that multiply together to make 19773 are 3 x 3 x 13 x 13 x 13. When we strip out the pairs only, we get 3 x 3 x 13 x 13 = 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Divide 19773 by the number (A) squared. 39 squared is 1521 and 19773 divided by 1521 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 19773 in its simplest radical form as follows:

√19773 = A√B

√19773 = 39√13

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