Simplify Square Root of 86704

Here we will show you two methods that you can use to simplify the square root of 86704. In other words, we will show you how to find the square root of 86704 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.

√86704 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 86704 to simplify the square root of 86704. 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 86704. The factors of 86704 are 1, 2, 4, 8, 16, 5419, 10838, 21676, 43352, and 86704. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 86704 divided by the greatest perfect square from the list of all factors of 86704. We determined above that the greatest perfect square from the list of all factors of 86704 is 16. Furthermore, 86704 divided by 16 is 5419, therefore B equals 5419.

Now we have A and B and can get our answer to 86704 in its simplest radical form as follows:

√86704 = A√B

√86704 = 4√5419

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 86704 to simplify the square root of 86704 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 86704 and then take the square root of that product. The prime factors that multiply together to make 86704 are 2 x 2 x 2 x 2 x 5419. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 86704 by the number (A) squared. 4 squared is 16 and 86704 divided by 16 is 5419. Therefore, B equals 5419.

Once again we have A and B and can get our answer to 86704 in its simplest radical form as follows:

√86704 = A√B

√86704 = 4√5419

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