Simplify Square Root of 3616

Here we will show you two methods that you can use to simplify the square root of 3616. In other words, we will show you how to find the square root of 3616 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.

√3616 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 3616 to simplify the square root of 3616. 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 3616. The factors of 3616 are 1, 2, 4, 8, 16, 32, 113, 226, 452, 904, 1808, and 3616. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 3616 divided by the greatest perfect square from the list of all factors of 3616. We determined above that the greatest perfect square from the list of all factors of 3616 is 16. Furthermore, 3616 divided by 16 is 226, therefore B equals 226.

Now we have A and B and can get our answer to 3616 in its simplest radical form as follows:

√3616 = A√B

√3616 = 4√226

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 3616 to simplify the square root of 3616 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 3616 and then take the square root of that product. The prime factors that multiply together to make 3616 are 2 x 2 x 2 x 2 x 2 x 113. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 3616 by the number (A) squared. 4 squared is 16 and 3616 divided by 16 is 226. Therefore, B equals 226.

Once again we have A and B and can get our answer to 3616 in its simplest radical form as follows:

√3616 = A√B

√3616 = 4√226

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Simplify Square Root of 3617
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