Simplify Square Root of 82152

Here we will show you two methods that you can use to simplify the square root of 82152. In other words, we will show you how to find the square root of 82152 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.

√82152 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 82152 to simplify the square root of 82152. 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 82152. The factors of 82152 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 163, 168, 252, 326, 489, 504, 652, 978, 1141, 1304, 1467, 1956, 2282, 2934, 3423, 3912, 4564, 5868, 6846, 9128, 10269, 11736, 13692, 20538, 27384, 41076, and 82152. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 82152 divided by the greatest perfect square from the list of all factors of 82152. We determined above that the greatest perfect square from the list of all factors of 82152 is 36. Furthermore, 82152 divided by 36 is 2282, therefore B equals 2282.

Now we have A and B and can get our answer to 82152 in its simplest radical form as follows:

√82152 = A√B

√82152 = 6√2282

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 82152 to simplify the square root of 82152 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 82152 and then take the square root of that product. The prime factors that multiply together to make 82152 are 2 x 2 x 2 x 3 x 3 x 7 x 163. 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 82152 by the number (A) squared. 6 squared is 36 and 82152 divided by 36 is 2282. Therefore, B equals 2282.

Once again we have A and B and can get our answer to 82152 in its simplest radical form as follows:

√82152 = A√B

√82152 = 6√2282

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