Simplify Square Root of 85140

Here we will show you two methods that you can use to simplify the square root of 85140. In other words, we will show you how to find the square root of 85140 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.

√85140 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 85140 to simplify the square root of 85140. 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 85140. The factors of 85140 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 43, 44, 45, 55, 60, 66, 86, 90, 99, 110, 129, 132, 165, 172, 180, 198, 215, 220, 258, 330, 387, 396, 430, 473, 495, 516, 645, 660, 774, 860, 946, 990, 1290, 1419, 1548, 1892, 1935, 1980, 2365, 2580, 2838, 3870, 4257, 4730, 5676, 7095, 7740, 8514, 9460, 14190, 17028, 21285, 28380, 42570, and 85140. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 85140 divided by the greatest perfect square from the list of all factors of 85140. We determined above that the greatest perfect square from the list of all factors of 85140 is 36. Furthermore, 85140 divided by 36 is 2365, therefore B equals 2365.

Now we have A and B and can get our answer to 85140 in its simplest radical form as follows:

√85140 = A√B

√85140 = 6√2365

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 85140 to simplify the square root of 85140 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 85140 and then take the square root of that product. The prime factors that multiply together to make 85140 are 2 x 2 x 3 x 3 x 5 x 11 x 43. 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 85140 by the number (A) squared. 6 squared is 36 and 85140 divided by 36 is 2365. Therefore, B equals 2365.

Once again we have A and B and can get our answer to 85140 in its simplest radical form as follows:

√85140 = A√B

√85140 = 6√2365

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