Simplify Square Root of 78125

Here we will show you two methods that you can use to simplify the square root of 78125. In other words, we will show you how to find the square root of 78125 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.

√78125 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78125 to simplify the square root of 78125. 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 78125. The factors of 78125 are 1, 5, 25, 125, 625, 3125, 15625, and 78125. Furthermore, the greatest perfect square on this list is 15625 and the square root of 15625 is 125. Therefore, A equals 125.

B = Calculate 78125 divided by the greatest perfect square from the list of all factors of 78125. We determined above that the greatest perfect square from the list of all factors of 78125 is 15625. Furthermore, 78125 divided by 15625 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 78125 in its simplest radical form as follows:

√78125 = A√B

√78125 = 125√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78125 to simplify the square root of 78125 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 78125 and then take the square root of that product. The prime factors that multiply together to make 78125 are 5 x 5 x 5 x 5 x 5 x 5 x 5. When we strip out the pairs only, we get 5 x 5 x 5 x 5 x 5 x 5 = 15625 and the square root of 15625 is 125. Therefore, A equals 125.

B = Divide 78125 by the number (A) squared. 125 squared is 15625 and 78125 divided by 15625 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 78125 in its simplest radical form as follows:

√78125 = A√B

√78125 = 125√5

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Simplify Square Root of 78126
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