Simplify Square Root of 78500

Here we will show you two methods that you can use to simplify the square root of 78500. In other words, we will show you how to find the square root of 78500 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.

√78500 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78500 to simplify the square root of 78500. 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 78500. The factors of 78500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 157, 250, 314, 500, 628, 785, 1570, 3140, 3925, 7850, 15700, 19625, 39250, and 78500. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 78500 divided by the greatest perfect square from the list of all factors of 78500. We determined above that the greatest perfect square from the list of all factors of 78500 is 100. Furthermore, 78500 divided by 100 is 785, therefore B equals 785.

Now we have A and B and can get our answer to 78500 in its simplest radical form as follows:

√78500 = A√B

√78500 = 10√785

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78500 to simplify the square root of 78500 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 78500 and then take the square root of that product. The prime factors that multiply together to make 78500 are 2 x 2 x 5 x 5 x 5 x 157. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 78500 by the number (A) squared. 10 squared is 100 and 78500 divided by 100 is 785. Therefore, B equals 785.

Once again we have A and B and can get our answer to 78500 in its simplest radical form as follows:

√78500 = A√B

√78500 = 10√785

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