Simplify Square Root of 86650

Here we will show you two methods that you can use to simplify the square root of 86650. In other words, we will show you how to find the square root of 86650 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.

√86650 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86650 to simplify the square root of 86650. 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 86650. The factors of 86650 are 1, 2, 5, 10, 25, 50, 1733, 3466, 8665, 17330, 43325, and 86650. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 86650 divided by the greatest perfect square from the list of all factors of 86650. We determined above that the greatest perfect square from the list of all factors of 86650 is 25. Furthermore, 86650 divided by 25 is 3466, therefore B equals 3466.

Now we have A and B and can get our answer to 86650 in its simplest radical form as follows:

√86650 = A√B

√86650 = 5√3466

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86650 to simplify the square root of 86650 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 86650 and then take the square root of that product. The prime factors that multiply together to make 86650 are 2 x 5 x 5 x 1733. 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 86650 by the number (A) squared. 5 squared is 25 and 86650 divided by 25 is 3466. Therefore, B equals 3466.

Once again we have A and B and can get our answer to 86650 in its simplest radical form as follows:

√86650 = A√B

√86650 = 5√3466

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Simplify Square Root of 86651
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