Simplify Square Root of 27184

Here we will show you two methods that you can use to simplify the square root of 27184. In other words, we will show you how to find the square root of 27184 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.

√27184 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 27184 to simplify the square root of 27184. 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 27184. The factors of 27184 are 1, 2, 4, 8, 16, 1699, 3398, 6796, 13592, and 27184. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 27184 divided by the greatest perfect square from the list of all factors of 27184. We determined above that the greatest perfect square from the list of all factors of 27184 is 16. Furthermore, 27184 divided by 16 is 1699, therefore B equals 1699.

Now we have A and B and can get our answer to 27184 in its simplest radical form as follows:

√27184 = A√B

√27184 = 4√1699

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 27184 to simplify the square root of 27184 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 27184 and then take the square root of that product. The prime factors that multiply together to make 27184 are 2 x 2 x 2 x 2 x 1699. 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 27184 by the number (A) squared. 4 squared is 16 and 27184 divided by 16 is 1699. Therefore, B equals 1699.

Once again we have A and B and can get our answer to 27184 in its simplest radical form as follows:

√27184 = A√B

√27184 = 4√1699

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Simplify Square Root of 27185
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