Simplify Square Root of 49152

Here we will show you two methods that you can use to simplify the square root of 49152. In other words, we will show you how to find the square root of 49152 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.

√49152 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 49152 to simplify the square root of 49152. 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 49152. The factors of 49152 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, and 49152. Furthermore, the greatest perfect square on this list is 16384 and the square root of 16384 is 128. Therefore, A equals 128.

B = Calculate 49152 divided by the greatest perfect square from the list of all factors of 49152. We determined above that the greatest perfect square from the list of all factors of 49152 is 16384. Furthermore, 49152 divided by 16384 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 49152 in its simplest radical form as follows:

√49152 = A√B

√49152 = 128√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 49152 to simplify the square root of 49152 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 49152 and then take the square root of that product. The prime factors that multiply together to make 49152 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3. 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 x 2 x 2 x 2 x 2 = 16384 and the square root of 16384 is 128. Therefore, A equals 128.

B = Divide 49152 by the number (A) squared. 128 squared is 16384 and 49152 divided by 16384 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 49152 in its simplest radical form as follows:

√49152 = A√B

√49152 = 128√3

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