Simplify Square Root of 77850

Here we will show you two methods that you can use to simplify the square root of 77850. In other words, we will show you how to find the square root of 77850 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.

√77850 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77850 to simplify the square root of 77850. 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 77850. The factors of 77850 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 173, 225, 346, 450, 519, 865, 1038, 1557, 1730, 2595, 3114, 4325, 5190, 7785, 8650, 12975, 15570, 25950, 38925, and 77850. Furthermore, the greatest perfect square on this list is 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Calculate 77850 divided by the greatest perfect square from the list of all factors of 77850. We determined above that the greatest perfect square from the list of all factors of 77850 is 225. Furthermore, 77850 divided by 225 is 346, therefore B equals 346.

Now we have A and B and can get our answer to 77850 in its simplest radical form as follows:

√77850 = A√B

√77850 = 15√346

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77850 to simplify the square root of 77850 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 77850 and then take the square root of that product. The prime factors that multiply together to make 77850 are 2 x 3 x 3 x 5 x 5 x 173. When we strip out the pairs only, we get 3 x 3 x 5 x 5 = 225 and the square root of 225 is 15. Therefore, A equals 15.

B = Divide 77850 by the number (A) squared. 15 squared is 225 and 77850 divided by 225 is 346. Therefore, B equals 346.

Once again we have A and B and can get our answer to 77850 in its simplest radical form as follows:

√77850 = A√B

√77850 = 15√346

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

Simplify Square Root of 77851
Here is the next square root on our list that we have simplifed for you.