Simplify Square Root of 38784

Here we will show you two methods that you can use to simplify the square root of 38784. In other words, we will show you how to find the square root of 38784 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.

√38784 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 38784 to simplify the square root of 38784. 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 38784. The factors of 38784 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 101, 128, 192, 202, 303, 384, 404, 606, 808, 1212, 1616, 2424, 3232, 4848, 6464, 9696, 12928, 19392, and 38784. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 38784 divided by the greatest perfect square from the list of all factors of 38784. We determined above that the greatest perfect square from the list of all factors of 38784 is 64. Furthermore, 38784 divided by 64 is 606, therefore B equals 606.

Now we have A and B and can get our answer to 38784 in its simplest radical form as follows:

√38784 = A√B

√38784 = 8√606

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 38784 to simplify the square root of 38784 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 38784 and then take the square root of that product. The prime factors that multiply together to make 38784 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 101. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 38784 by the number (A) squared. 8 squared is 64 and 38784 divided by 64 is 606. Therefore, B equals 606.

Once again we have A and B and can get our answer to 38784 in its simplest radical form as follows:

√38784 = A√B

√38784 = 8√606

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