Simplify Square Root of 38672

Here we will show you two methods that you can use to simplify the square root of 38672. In other words, we will show you how to find the square root of 38672 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.

√38672 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 38672 to simplify the square root of 38672. 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 38672. The factors of 38672 are 1, 2, 4, 8, 16, 2417, 4834, 9668, 19336, and 38672. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 38672 divided by the greatest perfect square from the list of all factors of 38672. We determined above that the greatest perfect square from the list of all factors of 38672 is 16. Furthermore, 38672 divided by 16 is 2417, therefore B equals 2417.

Now we have A and B and can get our answer to 38672 in its simplest radical form as follows:

√38672 = A√B

√38672 = 4√2417

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 38672 to simplify the square root of 38672 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 38672 and then take the square root of that product. The prime factors that multiply together to make 38672 are 2 x 2 x 2 x 2 x 2417. 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 38672 by the number (A) squared. 4 squared is 16 and 38672 divided by 16 is 2417. Therefore, B equals 2417.

Once again we have A and B and can get our answer to 38672 in its simplest radical form as follows:

√38672 = A√B

√38672 = 4√2417

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Simplify Square Root of 38673
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