Simplify Square Root of 50784

Here we will show you two methods that you can use to simplify the square root of 50784. In other words, we will show you how to find the square root of 50784 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.

√50784 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 50784 to simplify the square root of 50784. 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 50784. The factors of 50784 are 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 529, 552, 736, 1058, 1104, 1587, 2116, 2208, 3174, 4232, 6348, 8464, 12696, 16928, 25392, and 50784. Furthermore, the greatest perfect square on this list is 8464 and the square root of 8464 is 92. Therefore, A equals 92.

B = Calculate 50784 divided by the greatest perfect square from the list of all factors of 50784. We determined above that the greatest perfect square from the list of all factors of 50784 is 8464. Furthermore, 50784 divided by 8464 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 50784 in its simplest radical form as follows:

√50784 = A√B

√50784 = 92√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 50784 to simplify the square root of 50784 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 50784 and then take the square root of that product. The prime factors that multiply together to make 50784 are 2 x 2 x 2 x 2 x 2 x 3 x 23 x 23. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 23 x 23 = 8464 and the square root of 8464 is 92. Therefore, A equals 92.

B = Divide 50784 by the number (A) squared. 92 squared is 8464 and 50784 divided by 8464 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 50784 in its simplest radical form as follows:

√50784 = A√B

√50784 = 92√6

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