Simplify Square Root of 22576

Here we will show you two methods that you can use to simplify the square root of 22576. In other words, we will show you how to find the square root of 22576 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.

√22576 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 22576 to simplify the square root of 22576. 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 22576. The factors of 22576 are 1, 2, 4, 8, 16, 17, 34, 68, 83, 136, 166, 272, 332, 664, 1328, 1411, 2822, 5644, 11288, and 22576. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 22576 divided by the greatest perfect square from the list of all factors of 22576. We determined above that the greatest perfect square from the list of all factors of 22576 is 16. Furthermore, 22576 divided by 16 is 1411, therefore B equals 1411.

Now we have A and B and can get our answer to 22576 in its simplest radical form as follows:

√22576 = A√B

√22576 = 4√1411

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 22576 to simplify the square root of 22576 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 22576 and then take the square root of that product. The prime factors that multiply together to make 22576 are 2 x 2 x 2 x 2 x 17 x 83. 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 22576 by the number (A) squared. 4 squared is 16 and 22576 divided by 16 is 1411. Therefore, B equals 1411.

Once again we have A and B and can get our answer to 22576 in its simplest radical form as follows:

√22576 = A√B

√22576 = 4√1411

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Simplify Square Root of 22577
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