Simplify Square Root of 9702

Here we will show you two methods that you can use to simplify the square root of 9702. In other words, we will show you how to find the square root of 9702 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.

√9702 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 9702 to simplify the square root of 9702. 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 9702. The factors of 9702 are 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 49, 63, 66, 77, 98, 99, 126, 147, 154, 198, 231, 294, 441, 462, 539, 693, 882, 1078, 1386, 1617, 3234, 4851, and 9702. Furthermore, the greatest perfect square on this list is 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Calculate 9702 divided by the greatest perfect square from the list of all factors of 9702. We determined above that the greatest perfect square from the list of all factors of 9702 is 441. Furthermore, 9702 divided by 441 is 22, therefore B equals 22.

Now we have A and B and can get our answer to 9702 in its simplest radical form as follows:

√9702 = A√B

√9702 = 21√22

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 9702 to simplify the square root of 9702 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 9702 and then take the square root of that product. The prime factors that multiply together to make 9702 are 2 x 3 x 3 x 7 x 7 x 11. When we strip out the pairs only, we get 3 x 3 x 7 x 7 = 441 and the square root of 441 is 21. Therefore, A equals 21.

B = Divide 9702 by the number (A) squared. 21 squared is 441 and 9702 divided by 441 is 22. Therefore, B equals 22.

Once again we have A and B and can get our answer to 9702 in its simplest radical form as follows:

√9702 = A√B

√9702 = 21√22

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

Simplify Square Root of 9703
Here is the next square root on our list that we have simplifed for you.