Simplify Square Root of 38115

Here we will show you two methods that you can use to simplify the square root of 38115. In other words, we will show you how to find the square root of 38115 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.

√38115 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 38115 to simplify the square root of 38115. 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 38115. The factors of 38115 are 1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 121, 165, 231, 315, 363, 385, 495, 605, 693, 847, 1089, 1155, 1815, 2541, 3465, 4235, 5445, 7623, 12705, and 38115. Furthermore, the greatest perfect square on this list is 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Calculate 38115 divided by the greatest perfect square from the list of all factors of 38115. We determined above that the greatest perfect square from the list of all factors of 38115 is 1089. Furthermore, 38115 divided by 1089 is 35, therefore B equals 35.

Now we have A and B and can get our answer to 38115 in its simplest radical form as follows:

√38115 = A√B

√38115 = 33√35

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 38115 to simplify the square root of 38115 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 38115 and then take the square root of that product. The prime factors that multiply together to make 38115 are 3 x 3 x 5 x 7 x 11 x 11. When we strip out the pairs only, we get 3 x 3 x 11 x 11 = 1089 and the square root of 1089 is 33. Therefore, A equals 33.

B = Divide 38115 by the number (A) squared. 33 squared is 1089 and 38115 divided by 1089 is 35. Therefore, B equals 35.

Once again we have A and B and can get our answer to 38115 in its simplest radical form as follows:

√38115 = A√B

√38115 = 33√35

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