Simplify Square Root of 87184

Here we will show you two methods that you can use to simplify the square root of 87184. In other words, we will show you how to find the square root of 87184 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.

√87184 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 87184 to simplify the square root of 87184. 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 87184. The factors of 87184 are 1, 2, 4, 8, 16, 5449, 10898, 21796, 43592, and 87184. Furthermore, the greatest perfect square on this list is 16 and the square root of 16 is 4. Therefore, A equals 4.

B = Calculate 87184 divided by the greatest perfect square from the list of all factors of 87184. We determined above that the greatest perfect square from the list of all factors of 87184 is 16. Furthermore, 87184 divided by 16 is 5449, therefore B equals 5449.

Now we have A and B and can get our answer to 87184 in its simplest radical form as follows:

√87184 = A√B

√87184 = 4√5449

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 87184 to simplify the square root of 87184 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 87184 and then take the square root of that product. The prime factors that multiply together to make 87184 are 2 x 2 x 2 x 2 x 5449. 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 87184 by the number (A) squared. 4 squared is 16 and 87184 divided by 16 is 5449. Therefore, B equals 5449.

Once again we have A and B and can get our answer to 87184 in its simplest radical form as follows:

√87184 = A√B

√87184 = 4√5449

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Simplify Square Root of 87185
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