Simplify Square Root of 57344

Here we will show you two methods that you can use to simplify the square root of 57344. In other words, we will show you how to find the square root of 57344 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.

√57344 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 57344 to simplify the square root of 57344. 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 57344. The factors of 57344 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1024, 1792, 2048, 3584, 4096, 7168, 8192, 14336, 28672, and 57344. Furthermore, the greatest perfect square on this list is 4096 and the square root of 4096 is 64. Therefore, A equals 64.

B = Calculate 57344 divided by the greatest perfect square from the list of all factors of 57344. We determined above that the greatest perfect square from the list of all factors of 57344 is 4096. Furthermore, 57344 divided by 4096 is 14, therefore B equals 14.

Now we have A and B and can get our answer to 57344 in its simplest radical form as follows:

√57344 = A√B

√57344 = 64√14

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 57344 to simplify the square root of 57344 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 57344 and then take the square root of that product. The prime factors that multiply together to make 57344 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 7. 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 = 4096 and the square root of 4096 is 64. Therefore, A equals 64.

B = Divide 57344 by the number (A) squared. 64 squared is 4096 and 57344 divided by 4096 is 14. Therefore, B equals 14.

Once again we have A and B and can get our answer to 57344 in its simplest radical form as follows:

√57344 = A√B

√57344 = 64√14

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