Simplify Square Root of 90168

Here we will show you two methods that you can use to simplify the square root of 90168. In other words, we will show you how to find the square root of 90168 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.

√90168 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 90168 to simplify the square root of 90168. 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 90168. The factors of 90168 are 1, 2, 3, 4, 6, 8, 12, 13, 17, 24, 26, 34, 39, 51, 52, 68, 78, 102, 104, 136, 156, 204, 221, 289, 312, 408, 442, 578, 663, 867, 884, 1156, 1326, 1734, 1768, 2312, 2652, 3468, 3757, 5304, 6936, 7514, 11271, 15028, 22542, 30056, 45084, and 90168. Furthermore, the greatest perfect square on this list is 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Calculate 90168 divided by the greatest perfect square from the list of all factors of 90168. We determined above that the greatest perfect square from the list of all factors of 90168 is 1156. Furthermore, 90168 divided by 1156 is 78, therefore B equals 78.

Now we have A and B and can get our answer to 90168 in its simplest radical form as follows:

√90168 = A√B

√90168 = 34√78

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 90168 to simplify the square root of 90168 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 90168 and then take the square root of that product. The prime factors that multiply together to make 90168 are 2 x 2 x 2 x 3 x 13 x 17 x 17. When we strip out the pairs only, we get 2 x 2 x 17 x 17 = 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Divide 90168 by the number (A) squared. 34 squared is 1156 and 90168 divided by 1156 is 78. Therefore, B equals 78.

Once again we have A and B and can get our answer to 90168 in its simplest radical form as follows:

√90168 = A√B

√90168 = 34√78

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Simplify Square Root of 90169
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