Simplify Square Root of 78250

Here we will show you two methods that you can use to simplify the square root of 78250. In other words, we will show you how to find the square root of 78250 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.

√78250 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78250 to simplify the square root of 78250. 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 78250. The factors of 78250 are 1, 2, 5, 10, 25, 50, 125, 250, 313, 626, 1565, 3130, 7825, 15650, 39125, and 78250. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 78250 divided by the greatest perfect square from the list of all factors of 78250. We determined above that the greatest perfect square from the list of all factors of 78250 is 25. Furthermore, 78250 divided by 25 is 3130, therefore B equals 3130.

Now we have A and B and can get our answer to 78250 in its simplest radical form as follows:

√78250 = A√B

√78250 = 5√3130

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78250 to simplify the square root of 78250 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 78250 and then take the square root of that product. The prime factors that multiply together to make 78250 are 2 x 5 x 5 x 5 x 313. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 78250 by the number (A) squared. 5 squared is 25 and 78250 divided by 25 is 3130. Therefore, B equals 3130.

Once again we have A and B and can get our answer to 78250 in its simplest radical form as follows:

√78250 = A√B

√78250 = 5√3130

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Simplify Square Root of 78251
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