Simplify Square Root of 80217

Here we will show you two methods that you can use to simplify the square root of 80217. In other words, we will show you how to find the square root of 80217 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.

√80217 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 80217 to simplify the square root of 80217. 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 80217. The factors of 80217 are 1, 3, 9, 27, 2971, 8913, 26739, and 80217. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 80217 divided by the greatest perfect square from the list of all factors of 80217. We determined above that the greatest perfect square from the list of all factors of 80217 is 9. Furthermore, 80217 divided by 9 is 8913, therefore B equals 8913.

Now we have A and B and can get our answer to 80217 in its simplest radical form as follows:

√80217 = A√B

√80217 = 3√8913

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 80217 to simplify the square root of 80217 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 80217 and then take the square root of that product. The prime factors that multiply together to make 80217 are 3 x 3 x 3 x 2971. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 80217 by the number (A) squared. 3 squared is 9 and 80217 divided by 9 is 8913. Therefore, B equals 8913.

Once again we have A and B and can get our answer to 80217 in its simplest radical form as follows:

√80217 = A√B

√80217 = 3√8913

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Simplify Square Root of 80218
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