Simplify Square Root of 60552

Here we will show you two methods that you can use to simplify the square root of 60552. In other words, we will show you how to find the square root of 60552 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.

√60552 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60552 to simplify the square root of 60552. 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 60552. The factors of 60552 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 29, 36, 58, 72, 87, 116, 174, 232, 261, 348, 522, 696, 841, 1044, 1682, 2088, 2523, 3364, 5046, 6728, 7569, 10092, 15138, 20184, 30276, and 60552. Furthermore, the greatest perfect square on this list is 30276 and the square root of 30276 is 174. Therefore, A equals 174.

B = Calculate 60552 divided by the greatest perfect square from the list of all factors of 60552. We determined above that the greatest perfect square from the list of all factors of 60552 is 30276. Furthermore, 60552 divided by 30276 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 60552 in its simplest radical form as follows:

√60552 = A√B

√60552 = 174√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60552 to simplify the square root of 60552 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 60552 and then take the square root of that product. The prime factors that multiply together to make 60552 are 2 x 2 x 2 x 3 x 3 x 29 x 29. When we strip out the pairs only, we get 2 x 2 x 3 x 3 x 29 x 29 = 30276 and the square root of 30276 is 174. Therefore, A equals 174.

B = Divide 60552 by the number (A) squared. 174 squared is 30276 and 60552 divided by 30276 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 60552 in its simplest radical form as follows:

√60552 = A√B

√60552 = 174√2

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Simplify Square Root of 60553
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