Simplify Square Root of 2048

Here we will show you two methods that you can use to simplify the square root of 2048. In other words, we will show you how to find the square root of 2048 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.

√2048 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2048 to simplify the square root of 2048. 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 2048. The factors of 2048 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and 2048. Furthermore, the greatest perfect square on this list is 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Calculate 2048 divided by the greatest perfect square from the list of all factors of 2048. We determined above that the greatest perfect square from the list of all factors of 2048 is 1024. Furthermore, 2048 divided by 1024 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 2048 in its simplest radical form as follows:

√2048 = A√B

√2048 = 32√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2048 to simplify the square root of 2048 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 2048 and then take the square root of that product. The prime factors that multiply together to make 2048 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024 and the square root of 1024 is 32. Therefore, A equals 32.

B = Divide 2048 by the number (A) squared. 32 squared is 1024 and 2048 divided by 1024 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 2048 in its simplest radical form as follows:

√2048 = A√B

√2048 = 32√2

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Simplify Square Root of 2049
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