Simplify Square Root of 77800

Here we will show you two methods that you can use to simplify the square root of 77800. In other words, we will show you how to find the square root of 77800 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.

√77800 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 77800 to simplify the square root of 77800. 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 77800. The factors of 77800 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 389, 778, 1556, 1945, 3112, 3890, 7780, 9725, 15560, 19450, 38900, and 77800. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 77800 divided by the greatest perfect square from the list of all factors of 77800. We determined above that the greatest perfect square from the list of all factors of 77800 is 100. Furthermore, 77800 divided by 100 is 778, therefore B equals 778.

Now we have A and B and can get our answer to 77800 in its simplest radical form as follows:

√77800 = A√B

√77800 = 10√778

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 77800 to simplify the square root of 77800 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 77800 and then take the square root of that product. The prime factors that multiply together to make 77800 are 2 x 2 x 2 x 5 x 5 x 389. 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 77800 by the number (A) squared. 10 squared is 100 and 77800 divided by 100 is 778. Therefore, B equals 778.

Once again we have A and B and can get our answer to 77800 in its simplest radical form as follows:

√77800 = A√B

√77800 = 10√778

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