Simplify Square Root of 55152

Here we will show you two methods that you can use to simplify the square root of 55152. In other words, we will show you how to find the square root of 55152 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.

√55152 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55152 to simplify the square root of 55152. 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 55152. The factors of 55152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 383, 766, 1149, 1532, 2298, 3064, 3447, 4596, 6128, 6894, 9192, 13788, 18384, 27576, and 55152. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 55152 divided by the greatest perfect square from the list of all factors of 55152. We determined above that the greatest perfect square from the list of all factors of 55152 is 144. Furthermore, 55152 divided by 144 is 383, therefore B equals 383.

Now we have A and B and can get our answer to 55152 in its simplest radical form as follows:

√55152 = A√B

√55152 = 12√383

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55152 to simplify the square root of 55152 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 55152 and then take the square root of that product. The prime factors that multiply together to make 55152 are 2 x 2 x 2 x 2 x 3 x 3 x 383. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 55152 by the number (A) squared. 12 squared is 144 and 55152 divided by 144 is 383. Therefore, B equals 383.

Once again we have A and B and can get our answer to 55152 in its simplest radical form as follows:

√55152 = A√B

√55152 = 12√383

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