
Here we will show you two methods that you can use to simplify the square root of 86418. In other words, we will show you how to find the square root of 86418 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.
√86418 = A√B
Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86418 to simplify the square root of 86418. 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 86418. The factors of 86418 are 1, 2, 3, 6, 9, 18, 4801, 9602, 14403, 28806, 43209, and 86418. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.
B = Calculate 86418 divided by the greatest perfect square from the list of all factors of 86418. We determined above that the greatest perfect square from the list of all factors of 86418 is 9. Furthermore, 86418 divided by 9 is 9602, therefore B equals 9602.
Now we have A and B and can get our answer to 86418 in its simplest radical form as follows:
√86418 = A√B
√86418 = 3√9602
Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86418 to simplify the square root of 86418 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 86418 and then take the square root of that product. The prime factors that multiply together to make 86418 are 2 x 3 x 3 x 4801. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.
B = Divide 86418 by the number (A) squared. 3 squared is 9 and 86418 divided by 9 is 9602. Therefore, B equals 9602.
Once again we have A and B and can get our answer to 86418 in its simplest radical form as follows:
√86418 = A√B
√86418 = 3√9602
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Simplify Square Root of 86419
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