Simplify Square Root of 35912

Here we will show you two methods that you can use to simplify the square root of 35912. In other words, we will show you how to find the square root of 35912 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.

√35912 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 35912 to simplify the square root of 35912. 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 35912. The factors of 35912 are 1, 2, 4, 8, 67, 134, 268, 536, 4489, 8978, 17956, and 35912. Furthermore, the greatest perfect square on this list is 17956 and the square root of 17956 is 134. Therefore, A equals 134.

B = Calculate 35912 divided by the greatest perfect square from the list of all factors of 35912. We determined above that the greatest perfect square from the list of all factors of 35912 is 17956. Furthermore, 35912 divided by 17956 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 35912 in its simplest radical form as follows:

√35912 = A√B

√35912 = 134√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 35912 to simplify the square root of 35912 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 35912 and then take the square root of that product. The prime factors that multiply together to make 35912 are 2 x 2 x 2 x 67 x 67. When we strip out the pairs only, we get 2 x 2 x 67 x 67 = 17956 and the square root of 17956 is 134. Therefore, A equals 134.

B = Divide 35912 by the number (A) squared. 134 squared is 17956 and 35912 divided by 17956 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 35912 in its simplest radical form as follows:

√35912 = A√B

√35912 = 134√2

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Simplify Square Root of 35913
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