Simplify Square Root of 4563

Here we will show you two methods that you can use to simplify the square root of 4563. In other words, we will show you how to find the square root of 4563 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.

√4563 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 4563 to simplify the square root of 4563. 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 4563. The factors of 4563 are 1, 3, 9, 13, 27, 39, 117, 169, 351, 507, 1521, and 4563. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 4563 divided by the greatest perfect square from the list of all factors of 4563. We determined above that the greatest perfect square from the list of all factors of 4563 is 1521. Furthermore, 4563 divided by 1521 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 4563 in its simplest radical form as follows:

√4563 = A√B

√4563 = 39√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 4563 to simplify the square root of 4563 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 4563 and then take the square root of that product. The prime factors that multiply together to make 4563 are 3 x 3 x 3 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 4563 by the number (A) squared. 39 squared is 1521 and 4563 divided by 1521 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 4563 in its simplest radical form as follows:

√4563 = A√B

√4563 = 39√3

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