Simplify Square Root of 78892

Here we will show you two methods that you can use to simplify the square root of 78892. In other words, we will show you how to find the square root of 78892 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.

√78892 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78892 to simplify the square root of 78892. 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 78892. The factors of 78892 are 1, 2, 4, 11, 22, 44, 121, 163, 242, 326, 484, 652, 1793, 3586, 7172, 19723, 39446, and 78892. Furthermore, the greatest perfect square on this list is 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Calculate 78892 divided by the greatest perfect square from the list of all factors of 78892. We determined above that the greatest perfect square from the list of all factors of 78892 is 484. Furthermore, 78892 divided by 484 is 163, therefore B equals 163.

Now we have A and B and can get our answer to 78892 in its simplest radical form as follows:

√78892 = A√B

√78892 = 22√163

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78892 to simplify the square root of 78892 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 78892 and then take the square root of that product. The prime factors that multiply together to make 78892 are 2 x 2 x 11 x 11 x 163. When we strip out the pairs only, we get 2 x 2 x 11 x 11 = 484 and the square root of 484 is 22. Therefore, A equals 22.

B = Divide 78892 by the number (A) squared. 22 squared is 484 and 78892 divided by 484 is 163. Therefore, B equals 163.

Once again we have A and B and can get our answer to 78892 in its simplest radical form as follows:

√78892 = A√B

√78892 = 22√163

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Simplify Square Root of 78893
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