Simplify Square Root of 5544

Here we will show you two methods that you can use to simplify the square root of 5544. In other words, we will show you how to find the square root of 5544 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.

√5544 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 5544 to simplify the square root of 5544. 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 5544. The factors of 5544 are 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 18, 21, 22, 24, 28, 33, 36, 42, 44, 56, 63, 66, 72, 77, 84, 88, 99, 126, 132, 154, 168, 198, 231, 252, 264, 308, 396, 462, 504, 616, 693, 792, 924, 1386, 1848, 2772, and 5544. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 5544 divided by the greatest perfect square from the list of all factors of 5544. We determined above that the greatest perfect square from the list of all factors of 5544 is 36. Furthermore, 5544 divided by 36 is 154, therefore B equals 154.

Now we have A and B and can get our answer to 5544 in its simplest radical form as follows:

√5544 = A√B

√5544 = 6√154

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 5544 to simplify the square root of 5544 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 5544 and then take the square root of that product. The prime factors that multiply together to make 5544 are 2 x 2 x 2 x 3 x 3 x 7 x 11. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 5544 by the number (A) squared. 6 squared is 36 and 5544 divided by 36 is 154. Therefore, B equals 154.

Once again we have A and B and can get our answer to 5544 in its simplest radical form as follows:

√5544 = A√B

√5544 = 6√154

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