Simplify Square Root of 54400

Here we will show you two methods that you can use to simplify the square root of 54400. In other words, we will show you how to find the square root of 54400 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.

√54400 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54400 to simplify the square root of 54400. 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 54400. The factors of 54400 are 1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 64, 68, 80, 85, 100, 128, 136, 160, 170, 200, 272, 320, 340, 400, 425, 544, 640, 680, 800, 850, 1088, 1360, 1600, 1700, 2176, 2720, 3200, 3400, 5440, 6800, 10880, 13600, 27200, and 54400. Furthermore, the greatest perfect square on this list is 1600 and the square root of 1600 is 40. Therefore, A equals 40.

B = Calculate 54400 divided by the greatest perfect square from the list of all factors of 54400. We determined above that the greatest perfect square from the list of all factors of 54400 is 1600. Furthermore, 54400 divided by 1600 is 34, therefore B equals 34.

Now we have A and B and can get our answer to 54400 in its simplest radical form as follows:

√54400 = A√B

√54400 = 40√34

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54400 to simplify the square root of 54400 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 54400 and then take the square root of that product. The prime factors that multiply together to make 54400 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 = 1600 and the square root of 1600 is 40. Therefore, A equals 40.

B = Divide 54400 by the number (A) squared. 40 squared is 1600 and 54400 divided by 1600 is 34. Therefore, B equals 34.

Once again we have A and B and can get our answer to 54400 in its simplest radical form as follows:

√54400 = A√B

√54400 = 40√34

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