Simplify Square Root of 11163

Here we will show you two methods that you can use to simplify the square root of 11163. In other words, we will show you how to find the square root of 11163 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.

√11163 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 11163 to simplify the square root of 11163. 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 11163. The factors of 11163 are 1, 3, 61, 183, 3721, and 11163. Furthermore, the greatest perfect square on this list is 3721 and the square root of 3721 is 61. Therefore, A equals 61.

B = Calculate 11163 divided by the greatest perfect square from the list of all factors of 11163. We determined above that the greatest perfect square from the list of all factors of 11163 is 3721. Furthermore, 11163 divided by 3721 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 11163 in its simplest radical form as follows:

√11163 = A√B

√11163 = 61√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 11163 to simplify the square root of 11163 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 11163 and then take the square root of that product. The prime factors that multiply together to make 11163 are 3 x 61 x 61. When we strip out the pairs only, we get 61 x 61 = 3721 and the square root of 3721 is 61. Therefore, A equals 61.

B = Divide 11163 by the number (A) squared. 61 squared is 3721 and 11163 divided by 3721 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 11163 in its simplest radical form as follows:

√11163 = A√B

√11163 = 61√3

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Simplify Square Root of 11164
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