Simplify Square Root of 10647

Here we will show you two methods that you can use to simplify the square root of 10647. In other words, we will show you how to find the square root of 10647 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.

√10647 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10647 to simplify the square root of 10647. 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 10647. The factors of 10647 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 169, 273, 507, 819, 1183, 1521, 3549, and 10647. Furthermore, the greatest perfect square on this list is 1521 and the square root of 1521 is 39. Therefore, A equals 39.

B = Calculate 10647 divided by the greatest perfect square from the list of all factors of 10647. We determined above that the greatest perfect square from the list of all factors of 10647 is 1521. Furthermore, 10647 divided by 1521 is 7, therefore B equals 7.

Now we have A and B and can get our answer to 10647 in its simplest radical form as follows:

√10647 = A√B

√10647 = 39√7

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10647 to simplify the square root of 10647 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 10647 and then take the square root of that product. The prime factors that multiply together to make 10647 are 3 x 3 x 7 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 10647 by the number (A) squared. 39 squared is 1521 and 10647 divided by 1521 is 7. Therefore, B equals 7.

Once again we have A and B and can get our answer to 10647 in its simplest radical form as follows:

√10647 = A√B

√10647 = 39√7

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Simplify Square Root of 10648
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