Simplify Square Root of 20628

Here we will show you two methods that you can use to simplify the square root of 20628. In other words, we will show you how to find the square root of 20628 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.

√20628 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 20628 to simplify the square root of 20628. 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 20628. The factors of 20628 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 191, 382, 573, 764, 1146, 1719, 2292, 3438, 5157, 6876, 10314, and 20628. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 20628 divided by the greatest perfect square from the list of all factors of 20628. We determined above that the greatest perfect square from the list of all factors of 20628 is 36. Furthermore, 20628 divided by 36 is 573, therefore B equals 573.

Now we have A and B and can get our answer to 20628 in its simplest radical form as follows:

√20628 = A√B

√20628 = 6√573

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 20628 to simplify the square root of 20628 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 20628 and then take the square root of that product. The prime factors that multiply together to make 20628 are 2 x 2 x 3 x 3 x 3 x 191. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 20628 by the number (A) squared. 6 squared is 36 and 20628 divided by 36 is 573. Therefore, B equals 573.

Once again we have A and B and can get our answer to 20628 in its simplest radical form as follows:

√20628 = A√B

√20628 = 6√573

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Simplify Square Root of 20629
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