Simplify Square Root of 10752

Here we will show you two methods that you can use to simplify the square root of 10752. In other words, we will show you how to find the square root of 10752 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.

√10752 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10752 to simplify the square root of 10752. 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 10752. The factors of 10752 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 128, 168, 192, 224, 256, 336, 384, 448, 512, 672, 768, 896, 1344, 1536, 1792, 2688, 3584, 5376, and 10752. Furthermore, the greatest perfect square on this list is 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Calculate 10752 divided by the greatest perfect square from the list of all factors of 10752. We determined above that the greatest perfect square from the list of all factors of 10752 is 256. Furthermore, 10752 divided by 256 is 42, therefore B equals 42.

Now we have A and B and can get our answer to 10752 in its simplest radical form as follows:

√10752 = A√B

√10752 = 16√42

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10752 to simplify the square root of 10752 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 10752 and then take the square root of that product. The prime factors that multiply together to make 10752 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 and the square root of 256 is 16. Therefore, A equals 16.

B = Divide 10752 by the number (A) squared. 16 squared is 256 and 10752 divided by 256 is 42. Therefore, B equals 42.

Once again we have A and B and can get our answer to 10752 in its simplest radical form as follows:

√10752 = A√B

√10752 = 16√42

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