Simplify Square Root of 11142

Here we will show you two methods that you can use to simplify the square root of 11142. In other words, we will show you how to find the square root of 11142 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.

√11142 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 11142 to simplify the square root of 11142. 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 11142. The factors of 11142 are 1, 2, 3, 6, 9, 18, 619, 1238, 1857, 3714, 5571, and 11142. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 11142 divided by the greatest perfect square from the list of all factors of 11142. We determined above that the greatest perfect square from the list of all factors of 11142 is 9. Furthermore, 11142 divided by 9 is 1238, therefore B equals 1238.

Now we have A and B and can get our answer to 11142 in its simplest radical form as follows:

√11142 = A√B

√11142 = 3√1238

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 11142 to simplify the square root of 11142 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 11142 and then take the square root of that product. The prime factors that multiply together to make 11142 are 2 x 3 x 3 x 619. 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 11142 by the number (A) squared. 3 squared is 9 and 11142 divided by 9 is 1238. Therefore, B equals 1238.

Once again we have A and B and can get our answer to 11142 in its simplest radical form as follows:

√11142 = A√B

√11142 = 3√1238

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 11143
Here is the next square root on our list that we have simplifed for you.