Simplify Square Root of 14013

Here we will show you two methods that you can use to simplify the square root of 14013. In other words, we will show you how to find the square root of 14013 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.

√14013 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 14013 to simplify the square root of 14013. 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 14013. The factors of 14013 are 1, 3, 9, 27, 81, 173, 519, 1557, 4671, and 14013. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 14013 divided by the greatest perfect square from the list of all factors of 14013. We determined above that the greatest perfect square from the list of all factors of 14013 is 81. Furthermore, 14013 divided by 81 is 173, therefore B equals 173.

Now we have A and B and can get our answer to 14013 in its simplest radical form as follows:

√14013 = A√B

√14013 = 9√173

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 14013 to simplify the square root of 14013 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 14013 and then take the square root of that product. The prime factors that multiply together to make 14013 are 3 x 3 x 3 x 3 x 173. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 14013 by the number (A) squared. 9 squared is 81 and 14013 divided by 81 is 173. Therefore, B equals 173.

Once again we have A and B and can get our answer to 14013 in its simplest radical form as follows:

√14013 = A√B

√14013 = 9√173

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Simplify Square Root of 14014
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