Simplify Square Root of 68376

Here we will show you two methods that you can use to simplify the square root of 68376. In other words, we will show you how to find the square root of 68376 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.

√68376 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 68376 to simplify the square root of 68376. 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 68376. The factors of 68376 are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 37, 42, 44, 56, 66, 74, 77, 84, 88, 111, 132, 148, 154, 168, 222, 231, 259, 264, 296, 308, 407, 444, 462, 518, 616, 777, 814, 888, 924, 1036, 1221, 1554, 1628, 1848, 2072, 2442, 2849, 3108, 3256, 4884, 5698, 6216, 8547, 9768, 11396, 17094, 22792, 34188, and 68376. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 68376 divided by the greatest perfect square from the list of all factors of 68376. We determined above that the greatest perfect square from the list of all factors of 68376 is 4. Furthermore, 68376 divided by 4 is 17094, therefore B equals 17094.

Now we have A and B and can get our answer to 68376 in its simplest radical form as follows:

√68376 = A√B

√68376 = 2√17094

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 68376 to simplify the square root of 68376 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 68376 and then take the square root of that product. The prime factors that multiply together to make 68376 are 2 x 2 x 2 x 3 x 7 x 11 x 37. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 68376 by the number (A) squared. 2 squared is 4 and 68376 divided by 4 is 17094. Therefore, B equals 17094.

Once again we have A and B and can get our answer to 68376 in its simplest radical form as follows:

√68376 = A√B

√68376 = 2√17094

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