Simplify Square Root of 20416

Here we will show you two methods that you can use to simplify the square root of 20416. In other words, we will show you how to find the square root of 20416 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.

√20416 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 20416 to simplify the square root of 20416. 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 20416. The factors of 20416 are 1, 2, 4, 8, 11, 16, 22, 29, 32, 44, 58, 64, 88, 116, 176, 232, 319, 352, 464, 638, 704, 928, 1276, 1856, 2552, 5104, 10208, and 20416. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 20416 divided by the greatest perfect square from the list of all factors of 20416. We determined above that the greatest perfect square from the list of all factors of 20416 is 64. Furthermore, 20416 divided by 64 is 319, therefore B equals 319.

Now we have A and B and can get our answer to 20416 in its simplest radical form as follows:

√20416 = A√B

√20416 = 8√319

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 20416 to simplify the square root of 20416 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 20416 and then take the square root of that product. The prime factors that multiply together to make 20416 are 2 x 2 x 2 x 2 x 2 x 2 x 11 x 29. 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 20416 by the number (A) squared. 8 squared is 64 and 20416 divided by 64 is 319. Therefore, B equals 319.

Once again we have A and B and can get our answer to 20416 in its simplest radical form as follows:

√20416 = A√B

√20416 = 8√319

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Simplify Square Root of 20417
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