Simplify Square Root of 11907

Here we will show you two methods that you can use to simplify the square root of 11907. In other words, we will show you how to find the square root of 11907 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.

√11907 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 11907 to simplify the square root of 11907. 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 11907. The factors of 11907 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 243, 441, 567, 1323, 1701, 3969, and 11907. Furthermore, the greatest perfect square on this list is 3969 and the square root of 3969 is 63. Therefore, A equals 63.

B = Calculate 11907 divided by the greatest perfect square from the list of all factors of 11907. We determined above that the greatest perfect square from the list of all factors of 11907 is 3969. Furthermore, 11907 divided by 3969 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 11907 in its simplest radical form as follows:

√11907 = A√B

√11907 = 63√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 11907 to simplify the square root of 11907 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 11907 and then take the square root of that product. The prime factors that multiply together to make 11907 are 3 x 3 x 3 x 3 x 3 x 7 x 7. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 7 x 7 = 3969 and the square root of 3969 is 63. Therefore, A equals 63.

B = Divide 11907 by the number (A) squared. 63 squared is 3969 and 11907 divided by 3969 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 11907 in its simplest radical form as follows:

√11907 = A√B

√11907 = 63√3

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