Simplify Square Root of 38663

Here we will show you two methods that you can use to simplify the square root of 38663. In other words, we will show you how to find the square root of 38663 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.

√38663 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 38663 to simplify the square root of 38663. 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 38663. The factors of 38663 are 1, 23, 41, 943, 1681, and 38663. Furthermore, the greatest perfect square on this list is 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Calculate 38663 divided by the greatest perfect square from the list of all factors of 38663. We determined above that the greatest perfect square from the list of all factors of 38663 is 1681. Furthermore, 38663 divided by 1681 is 23, therefore B equals 23.

Now we have A and B and can get our answer to 38663 in its simplest radical form as follows:

√38663 = A√B

√38663 = 41√23

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 38663 to simplify the square root of 38663 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 38663 and then take the square root of that product. The prime factors that multiply together to make 38663 are 23 x 41 x 41. When we strip out the pairs only, we get 41 x 41 = 1681 and the square root of 1681 is 41. Therefore, A equals 41.

B = Divide 38663 by the number (A) squared. 41 squared is 1681 and 38663 divided by 1681 is 23. Therefore, B equals 23.

Once again we have A and B and can get our answer to 38663 in its simplest radical form as follows:

√38663 = A√B

√38663 = 41√23

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Simplify Square Root of 38664
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