Simplify Square Root of 69168

Here we will show you two methods that you can use to simplify the square root of 69168. In other words, we will show you how to find the square root of 69168 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.

√69168 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 69168 to simplify the square root of 69168. 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 69168. The factors of 69168 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 131, 132, 176, 262, 264, 393, 524, 528, 786, 1048, 1441, 1572, 2096, 2882, 3144, 4323, 5764, 6288, 8646, 11528, 17292, 23056, 34584, and 69168. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 69168 divided by the greatest perfect square from the list of all factors of 69168. We determined above that the greatest perfect square from the list of all factors of 69168 is 16. Furthermore, 69168 divided by 16 is 4323, therefore B equals 4323.

Now we have A and B and can get our answer to 69168 in its simplest radical form as follows:

√69168 = A√B

√69168 = 4√4323

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 69168 to simplify the square root of 69168 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 69168 and then take the square root of that product. The prime factors that multiply together to make 69168 are 2 x 2 x 2 x 2 x 3 x 11 x 131. When we strip out the pairs only, we get 2 x 2 x 2 x 2 = 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Divide 69168 by the number (A) squared. 4 squared is 16 and 69168 divided by 16 is 4323. Therefore, B equals 4323.

Once again we have A and B and can get our answer to 69168 in its simplest radical form as follows:

√69168 = A√B

√69168 = 4√4323

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Simplify Square Root of 69169
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