Simplify Square Root of 35838

Here we will show you two methods that you can use to simplify the square root of 35838. In other words, we will show you how to find the square root of 35838 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.

√35838 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 35838 to simplify the square root of 35838. 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 35838. The factors of 35838 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 181, 198, 362, 543, 1086, 1629, 1991, 3258, 3982, 5973, 11946, 17919, and 35838. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 35838 divided by the greatest perfect square from the list of all factors of 35838. We determined above that the greatest perfect square from the list of all factors of 35838 is 9. Furthermore, 35838 divided by 9 is 3982, therefore B equals 3982.

Now we have A and B and can get our answer to 35838 in its simplest radical form as follows:

√35838 = A√B

√35838 = 3√3982

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 35838 to simplify the square root of 35838 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 35838 and then take the square root of that product. The prime factors that multiply together to make 35838 are 2 x 3 x 3 x 11 x 181. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 35838 by the number (A) squared. 3 squared is 9 and 35838 divided by 9 is 3982. Therefore, B equals 3982.

Once again we have A and B and can get our answer to 35838 in its simplest radical form as follows:

√35838 = A√B

√35838 = 3√3982

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Simplify Square Root of 35839
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