Simplify Square Root of 17220

Here we will show you two methods that you can use to simplify the square root of 17220. In other words, we will show you how to find the square root of 17220 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.

√17220 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 17220 to simplify the square root of 17220. 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 17220. The factors of 17220 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 41, 42, 60, 70, 82, 84, 105, 123, 140, 164, 205, 210, 246, 287, 410, 420, 492, 574, 615, 820, 861, 1148, 1230, 1435, 1722, 2460, 2870, 3444, 4305, 5740, 8610, and 17220. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 17220 divided by the greatest perfect square from the list of all factors of 17220. We determined above that the greatest perfect square from the list of all factors of 17220 is 4. Furthermore, 17220 divided by 4 is 4305, therefore B equals 4305.

Now we have A and B and can get our answer to 17220 in its simplest radical form as follows:

√17220 = A√B

√17220 = 2√4305

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 17220 to simplify the square root of 17220 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 17220 and then take the square root of that product. The prime factors that multiply together to make 17220 are 2 x 2 x 3 x 5 x 7 x 41. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 17220 by the number (A) squared. 2 squared is 4 and 17220 divided by 4 is 4305. Therefore, B equals 4305.

Once again we have A and B and can get our answer to 17220 in its simplest radical form as follows:

√17220 = A√B

√17220 = 2√4305

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