Simplify Square Root of 92480

Here we will show you two methods that you can use to simplify the square root of 92480. In other words, we will show you how to find the square root of 92480 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.

√92480 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 92480 to simplify the square root of 92480. 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 92480. The factors of 92480 are 1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85, 136, 160, 170, 272, 289, 320, 340, 544, 578, 680, 1088, 1156, 1360, 1445, 2312, 2720, 2890, 4624, 5440, 5780, 9248, 11560, 18496, 23120, 46240, and 92480. Furthermore, the greatest perfect square on this list is 18496 and the square root of 18496 is 136. Therefore, A equals 136.

B = Calculate 92480 divided by the greatest perfect square from the list of all factors of 92480. We determined above that the greatest perfect square from the list of all factors of 92480 is 18496. Furthermore, 92480 divided by 18496 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 92480 in its simplest radical form as follows:

√92480 = A√B

√92480 = 136√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 92480 to simplify the square root of 92480 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 92480 and then take the square root of that product. The prime factors that multiply together to make 92480 are 2 x 2 x 2 x 2 x 2 x 2 x 5 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 17 x 17 = 18496 and the square root of 18496 is 136. Therefore, A equals 136.

B = Divide 92480 by the number (A) squared. 136 squared is 18496 and 92480 divided by 18496 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 92480 in its simplest radical form as follows:

√92480 = A√B

√92480 = 136√5

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