Simplify Square Root of 67431

Here we will show you two methods that you can use to simplify the square root of 67431. In other words, we will show you how to find the square root of 67431 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.

√67431 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 67431 to simplify the square root of 67431. 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 67431. The factors of 67431 are 1, 3, 7, 13, 19, 21, 39, 57, 91, 133, 169, 247, 273, 399, 507, 741, 1183, 1729, 3211, 3549, 5187, 9633, 22477, and 67431. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 67431 divided by the greatest perfect square from the list of all factors of 67431. We determined above that the greatest perfect square from the list of all factors of 67431 is 169. Furthermore, 67431 divided by 169 is 399, therefore B equals 399.

Now we have A and B and can get our answer to 67431 in its simplest radical form as follows:

√67431 = A√B

√67431 = 13√399

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 67431 to simplify the square root of 67431 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 67431 and then take the square root of that product. The prime factors that multiply together to make 67431 are 3 x 7 x 13 x 13 x 19. 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 67431 by the number (A) squared. 13 squared is 169 and 67431 divided by 169 is 399. Therefore, B equals 399.

Once again we have A and B and can get our answer to 67431 in its simplest radical form as follows:

√67431 = A√B

√67431 = 13√399

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

Simplify Square Root of 67432
Here is the next square root on our list that we have simplifed for you.