Simplify Square Root of 54384

Here we will show you two methods that you can use to simplify the square root of 54384. In other words, we will show you how to find the square root of 54384 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.

√54384 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 54384 to simplify the square root of 54384. 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 54384. The factors of 54384 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 103, 132, 176, 206, 264, 309, 412, 528, 618, 824, 1133, 1236, 1648, 2266, 2472, 3399, 4532, 4944, 6798, 9064, 13596, 18128, 27192, and 54384. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 54384 divided by the greatest perfect square from the list of all factors of 54384. We determined above that the greatest perfect square from the list of all factors of 54384 is 16. Furthermore, 54384 divided by 16 is 3399, therefore B equals 3399.

Now we have A and B and can get our answer to 54384 in its simplest radical form as follows:

√54384 = A√B

√54384 = 4√3399

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 54384 to simplify the square root of 54384 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 54384 and then take the square root of that product. The prime factors that multiply together to make 54384 are 2 x 2 x 2 x 2 x 3 x 11 x 103. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 54384 by the number (A) squared. 4 squared is 16 and 54384 divided by 16 is 3399. Therefore, B equals 3399.

Once again we have A and B and can get our answer to 54384 in its simplest radical form as follows:

√54384 = A√B

√54384 = 4√3399

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