Simplify Square Root of 96250

Here we will show you two methods that you can use to simplify the square root of 96250. In other words, we will show you how to find the square root of 96250 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.

√96250 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 96250 to simplify the square root of 96250. 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 96250. The factors of 96250 are 1, 2, 5, 7, 10, 11, 14, 22, 25, 35, 50, 55, 70, 77, 110, 125, 154, 175, 250, 275, 350, 385, 550, 625, 770, 875, 1250, 1375, 1750, 1925, 2750, 3850, 4375, 6875, 8750, 9625, 13750, 19250, 48125, and 96250. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 96250 divided by the greatest perfect square from the list of all factors of 96250. We determined above that the greatest perfect square from the list of all factors of 96250 is 625. Furthermore, 96250 divided by 625 is 154, therefore B equals 154.

Now we have A and B and can get our answer to 96250 in its simplest radical form as follows:

√96250 = A√B

√96250 = 25√154

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 96250 to simplify the square root of 96250 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 96250 and then take the square root of that product. The prime factors that multiply together to make 96250 are 2 x 5 x 5 x 5 x 5 x 7 x 11. When we strip out the pairs only, we get 5 x 5 x 5 x 5 = 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Divide 96250 by the number (A) squared. 25 squared is 625 and 96250 divided by 625 is 154. Therefore, B equals 154.

Once again we have A and B and can get our answer to 96250 in its simplest radical form as follows:

√96250 = A√B

√96250 = 25√154

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Simplify Square Root of 96251
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