Simplify Square Root of 84500

Here we will show you two methods that you can use to simplify the square root of 84500. In other words, we will show you how to find the square root of 84500 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.

√84500 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 84500 to simplify the square root of 84500. 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 84500. The factors of 84500 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 125, 130, 169, 250, 260, 325, 338, 500, 650, 676, 845, 1300, 1625, 1690, 3250, 3380, 4225, 6500, 8450, 16900, 21125, 42250, and 84500. Furthermore, the greatest perfect square on this list is 16900 and the square root of 16900 is 130. Therefore, A equals 130.

B = Calculate 84500 divided by the greatest perfect square from the list of all factors of 84500. We determined above that the greatest perfect square from the list of all factors of 84500 is 16900. Furthermore, 84500 divided by 16900 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 84500 in its simplest radical form as follows:

√84500 = A√B

√84500 = 130√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 84500 to simplify the square root of 84500 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 84500 and then take the square root of that product. The prime factors that multiply together to make 84500 are 2 x 2 x 5 x 5 x 5 x 13 x 13. When we strip out the pairs only, we get 2 x 2 x 5 x 5 x 13 x 13 = 16900 and the square root of 16900 is 130. Therefore, A equals 130.

B = Divide 84500 by the number (A) squared. 130 squared is 16900 and 84500 divided by 16900 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 84500 in its simplest radical form as follows:

√84500 = A√B

√84500 = 130√5

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