Simplify Square Root of 81209

Here we will show you two methods that you can use to simplify the square root of 81209. In other words, we will show you how to find the square root of 81209 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.

√81209 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81209 to simplify the square root of 81209. 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 81209. The factors of 81209 are 1, 17, 281, 289, 4777, and 81209. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 81209 divided by the greatest perfect square from the list of all factors of 81209. We determined above that the greatest perfect square from the list of all factors of 81209 is 289. Furthermore, 81209 divided by 289 is 281, therefore B equals 281.

Now we have A and B and can get our answer to 81209 in its simplest radical form as follows:

√81209 = A√B

√81209 = 17√281

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81209 to simplify the square root of 81209 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 81209 and then take the square root of that product. The prime factors that multiply together to make 81209 are 17 x 17 x 281. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 81209 by the number (A) squared. 17 squared is 289 and 81209 divided by 289 is 281. Therefore, B equals 281.

Once again we have A and B and can get our answer to 81209 in its simplest radical form as follows:

√81209 = A√B

√81209 = 17√281

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Simplify Square Root of 81210
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