Simplify Square Root of 10854

Here we will show you two methods that you can use to simplify the square root of 10854. In other words, we will show you how to find the square root of 10854 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.

√10854 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10854 to simplify the square root of 10854. 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 10854. The factors of 10854 are 1, 2, 3, 6, 9, 18, 27, 54, 67, 81, 134, 162, 201, 402, 603, 1206, 1809, 3618, 5427, and 10854. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 10854 divided by the greatest perfect square from the list of all factors of 10854. We determined above that the greatest perfect square from the list of all factors of 10854 is 81. Furthermore, 10854 divided by 81 is 134, therefore B equals 134.

Now we have A and B and can get our answer to 10854 in its simplest radical form as follows:

√10854 = A√B

√10854 = 9√134

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10854 to simplify the square root of 10854 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 10854 and then take the square root of that product. The prime factors that multiply together to make 10854 are 2 x 3 x 3 x 3 x 3 x 67. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 10854 by the number (A) squared. 9 squared is 81 and 10854 divided by 81 is 134. Therefore, B equals 134.

Once again we have A and B and can get our answer to 10854 in its simplest radical form as follows:

√10854 = A√B

√10854 = 9√134

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Simplify Square Root of 10855
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