Simplify Square Root of 55506

Here we will show you two methods that you can use to simplify the square root of 55506. In other words, we will show you how to find the square root of 55506 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.

√55506 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 55506 to simplify the square root of 55506. 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 55506. The factors of 55506 are 1, 2, 3, 6, 11, 22, 29, 33, 58, 66, 87, 174, 319, 638, 841, 957, 1682, 1914, 2523, 5046, 9251, 18502, 27753, and 55506. Furthermore, the greatest perfect square on this list is 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Calculate 55506 divided by the greatest perfect square from the list of all factors of 55506. We determined above that the greatest perfect square from the list of all factors of 55506 is 841. Furthermore, 55506 divided by 841 is 66, therefore B equals 66.

Now we have A and B and can get our answer to 55506 in its simplest radical form as follows:

√55506 = A√B

√55506 = 29√66

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 55506 to simplify the square root of 55506 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 55506 and then take the square root of that product. The prime factors that multiply together to make 55506 are 2 x 3 x 11 x 29 x 29. When we strip out the pairs only, we get 29 x 29 = 841 and the square root of 841 is 29. Therefore, A equals 29.

B = Divide 55506 by the number (A) squared. 29 squared is 841 and 55506 divided by 841 is 66. Therefore, B equals 66.

Once again we have A and B and can get our answer to 55506 in its simplest radical form as follows:

√55506 = A√B

√55506 = 29√66

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Simplify Square Root of 55507
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