Simplify Square Root of 60288

Here we will show you two methods that you can use to simplify the square root of 60288. In other words, we will show you how to find the square root of 60288 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.

√60288 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60288 to simplify the square root of 60288. 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 60288. The factors of 60288 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 157, 192, 314, 384, 471, 628, 942, 1256, 1884, 2512, 3768, 5024, 7536, 10048, 15072, 20096, 30144, and 60288. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 60288 divided by the greatest perfect square from the list of all factors of 60288. We determined above that the greatest perfect square from the list of all factors of 60288 is 64. Furthermore, 60288 divided by 64 is 942, therefore B equals 942.

Now we have A and B and can get our answer to 60288 in its simplest radical form as follows:

√60288 = A√B

√60288 = 8√942

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60288 to simplify the square root of 60288 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 60288 and then take the square root of that product. The prime factors that multiply together to make 60288 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 157. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 = 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Divide 60288 by the number (A) squared. 8 squared is 64 and 60288 divided by 64 is 942. Therefore, B equals 942.

Once again we have A and B and can get our answer to 60288 in its simplest radical form as follows:

√60288 = A√B

√60288 = 8√942

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