Simplify Square Root of 83430

Here we will show you two methods that you can use to simplify the square root of 83430. In other words, we will show you how to find the square root of 83430 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.

√83430 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 83430 to simplify the square root of 83430. 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 83430. The factors of 83430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 103, 135, 162, 206, 270, 309, 405, 515, 618, 810, 927, 1030, 1545, 1854, 2781, 3090, 4635, 5562, 8343, 9270, 13905, 16686, 27810, 41715, and 83430. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 83430 divided by the greatest perfect square from the list of all factors of 83430. We determined above that the greatest perfect square from the list of all factors of 83430 is 81. Furthermore, 83430 divided by 81 is 1030, therefore B equals 1030.

Now we have A and B and can get our answer to 83430 in its simplest radical form as follows:

√83430 = A√B

√83430 = 9√1030

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 83430 to simplify the square root of 83430 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 83430 and then take the square root of that product. The prime factors that multiply together to make 83430 are 2 x 3 x 3 x 3 x 3 x 5 x 103. 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 83430 by the number (A) squared. 9 squared is 81 and 83430 divided by 81 is 1030. Therefore, B equals 1030.

Once again we have A and B and can get our answer to 83430 in its simplest radical form as follows:

√83430 = A√B

√83430 = 9√1030

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

Simplify Square Root of 83431
Here is the next square root on our list that we have simplifed for you.