Simplify Square Root of 2197

Here we will show you two methods that you can use to simplify the square root of 2197. In other words, we will show you how to find the square root of 2197 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.

√2197 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 2197 to simplify the square root of 2197. 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 2197. The factors of 2197 are 1, 13, 169, and 2197. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 2197 divided by the greatest perfect square from the list of all factors of 2197. We determined above that the greatest perfect square from the list of all factors of 2197 is 169. Furthermore, 2197 divided by 169 is 13, therefore B equals 13.

Now we have A and B and can get our answer to 2197 in its simplest radical form as follows:

√2197 = A√B

√2197 = 13√13

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 2197 to simplify the square root of 2197 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 2197 and then take the square root of that product. The prime factors that multiply together to make 2197 are 13 x 13 x 13. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 2197 by the number (A) squared. 13 squared is 169 and 2197 divided by 169 is 13. Therefore, B equals 13.

Once again we have A and B and can get our answer to 2197 in its simplest radical form as follows:

√2197 = A√B

√2197 = 13√13

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Simplify Square Root of 2198
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