Simplify Square Root of 84708

Here we will show you two methods that you can use to simplify the square root of 84708. In other words, we will show you how to find the square root of 84708 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.

√84708 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84708 to simplify the square root of 84708. 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 84708. The factors of 84708 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 181, 234, 362, 468, 543, 724, 1086, 1629, 2172, 2353, 3258, 4706, 6516, 7059, 9412, 14118, 21177, 28236, 42354, and 84708. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 84708 divided by the greatest perfect square from the list of all factors of 84708. We determined above that the greatest perfect square from the list of all factors of 84708 is 36. Furthermore, 84708 divided by 36 is 2353, therefore B equals 2353.

Now we have A and B and can get our answer to 84708 in its simplest radical form as follows:

√84708 = A√B

√84708 = 6√2353

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84708 to simplify the square root of 84708 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 84708 and then take the square root of that product. The prime factors that multiply together to make 84708 are 2 x 2 x 3 x 3 x 13 x 181. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 84708 by the number (A) squared. 6 squared is 36 and 84708 divided by 36 is 2353. Therefore, B equals 2353.

Once again we have A and B and can get our answer to 84708 in its simplest radical form as follows:

√84708 = A√B

√84708 = 6√2353

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