Simplify Square Root of 81175

Here we will show you two methods that you can use to simplify the square root of 81175. In other words, we will show you how to find the square root of 81175 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.

√81175 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81175 to simplify the square root of 81175. 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 81175. The factors of 81175 are 1, 5, 17, 25, 85, 191, 425, 955, 3247, 4775, 16235, and 81175. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 81175 divided by the greatest perfect square from the list of all factors of 81175. We determined above that the greatest perfect square from the list of all factors of 81175 is 25. Furthermore, 81175 divided by 25 is 3247, therefore B equals 3247.

Now we have A and B and can get our answer to 81175 in its simplest radical form as follows:

√81175 = A√B

√81175 = 5√3247

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81175 to simplify the square root of 81175 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 81175 and then take the square root of that product. The prime factors that multiply together to make 81175 are 5 x 5 x 17 x 191. 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 81175 by the number (A) squared. 5 squared is 25 and 81175 divided by 25 is 3247. Therefore, B equals 3247.

Once again we have A and B and can get our answer to 81175 in its simplest radical form as follows:

√81175 = A√B

√81175 = 5√3247

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Simplify Square Root of 81176
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