Simplify Square Root of 10176

Here we will show you two methods that you can use to simplify the square root of 10176. In other words, we will show you how to find the square root of 10176 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.

√10176 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10176 to simplify the square root of 10176. 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 10176. The factors of 10176 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 53, 64, 96, 106, 159, 192, 212, 318, 424, 636, 848, 1272, 1696, 2544, 3392, 5088, and 10176. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 10176 divided by the greatest perfect square from the list of all factors of 10176. We determined above that the greatest perfect square from the list of all factors of 10176 is 64. Furthermore, 10176 divided by 64 is 159, therefore B equals 159.

Now we have A and B and can get our answer to 10176 in its simplest radical form as follows:

√10176 = A√B

√10176 = 8√159

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10176 to simplify the square root of 10176 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 10176 and then take the square root of that product. The prime factors that multiply together to make 10176 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 53. 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 10176 by the number (A) squared. 8 squared is 64 and 10176 divided by 64 is 159. Therefore, B equals 159.

Once again we have A and B and can get our answer to 10176 in its simplest radical form as follows:

√10176 = A√B

√10176 = 8√159

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Simplify Square Root of 10177
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