Simplify Square Root of 6384

Here we will show you two methods that you can use to simplify the square root of 6384. In other words, we will show you how to find the square root of 6384 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.

√6384 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 6384 to simplify the square root of 6384. 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 6384. The factors of 6384 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 19, 21, 24, 28, 38, 42, 48, 56, 57, 76, 84, 112, 114, 133, 152, 168, 228, 266, 304, 336, 399, 456, 532, 798, 912, 1064, 1596, 2128, 3192, and 6384. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 6384 divided by the greatest perfect square from the list of all factors of 6384. We determined above that the greatest perfect square from the list of all factors of 6384 is 16. Furthermore, 6384 divided by 16 is 399, therefore B equals 399.

Now we have A and B and can get our answer to 6384 in its simplest radical form as follows:

√6384 = A√B

√6384 = 4√399

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 6384 to simplify the square root of 6384 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 6384 and then take the square root of that product. The prime factors that multiply together to make 6384 are 2 x 2 x 2 x 2 x 3 x 7 x 19. 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 6384 by the number (A) squared. 4 squared is 16 and 6384 divided by 16 is 399. Therefore, B equals 399.

Once again we have A and B and can get our answer to 6384 in its simplest radical form as follows:

√6384 = A√B

√6384 = 4√399

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