Simplify Square Root of 82250

Here we will show you two methods that you can use to simplify the square root of 82250. In other words, we will show you how to find the square root of 82250 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.

√82250 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82250 to simplify the square root of 82250. 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 82250. The factors of 82250 are 1, 2, 5, 7, 10, 14, 25, 35, 47, 50, 70, 94, 125, 175, 235, 250, 329, 350, 470, 658, 875, 1175, 1645, 1750, 2350, 3290, 5875, 8225, 11750, 16450, 41125, and 82250. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 82250 divided by the greatest perfect square from the list of all factors of 82250. We determined above that the greatest perfect square from the list of all factors of 82250 is 25. Furthermore, 82250 divided by 25 is 3290, therefore B equals 3290.

Now we have A and B and can get our answer to 82250 in its simplest radical form as follows:

√82250 = A√B

√82250 = 5√3290

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82250 to simplify the square root of 82250 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 82250 and then take the square root of that product. The prime factors that multiply together to make 82250 are 2 x 5 x 5 x 5 x 7 x 47. 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 82250 by the number (A) squared. 5 squared is 25 and 82250 divided by 25 is 3290. Therefore, B equals 3290.

Once again we have A and B and can get our answer to 82250 in its simplest radical form as follows:

√82250 = A√B

√82250 = 5√3290

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Simplify Square Root of 82251
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