Simplify Square Root of 85850

Here we will show you two methods that you can use to simplify the square root of 85850. In other words, we will show you how to find the square root of 85850 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.

√85850 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85850 to simplify the square root of 85850. 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 85850. The factors of 85850 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 101, 170, 202, 425, 505, 850, 1010, 1717, 2525, 3434, 5050, 8585, 17170, 42925, and 85850. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 85850 divided by the greatest perfect square from the list of all factors of 85850. We determined above that the greatest perfect square from the list of all factors of 85850 is 25. Furthermore, 85850 divided by 25 is 3434, therefore B equals 3434.

Now we have A and B and can get our answer to 85850 in its simplest radical form as follows:

√85850 = A√B

√85850 = 5√3434

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85850 to simplify the square root of 85850 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 85850 and then take the square root of that product. The prime factors that multiply together to make 85850 are 2 x 5 x 5 x 17 x 101. 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 85850 by the number (A) squared. 5 squared is 25 and 85850 divided by 25 is 3434. Therefore, B equals 3434.

Once again we have A and B and can get our answer to 85850 in its simplest radical form as follows:

√85850 = A√B

√85850 = 5√3434

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Simplify Square Root of 85851
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