Simplify Square Root of 41664

Here we will show you two methods that you can use to simplify the square root of 41664. In other words, we will show you how to find the square root of 41664 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.

√41664 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 41664 to simplify the square root of 41664. 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 41664. The factors of 41664 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 31, 32, 42, 48, 56, 62, 64, 84, 93, 96, 112, 124, 168, 186, 192, 217, 224, 248, 336, 372, 434, 448, 496, 651, 672, 744, 868, 992, 1302, 1344, 1488, 1736, 1984, 2604, 2976, 3472, 5208, 5952, 6944, 10416, 13888, 20832, and 41664. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 41664 divided by the greatest perfect square from the list of all factors of 41664. We determined above that the greatest perfect square from the list of all factors of 41664 is 64. Furthermore, 41664 divided by 64 is 651, therefore B equals 651.

Now we have A and B and can get our answer to 41664 in its simplest radical form as follows:

√41664 = A√B

√41664 = 8√651

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 41664 to simplify the square root of 41664 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 41664 and then take the square root of that product. The prime factors that multiply together to make 41664 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 31. 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 41664 by the number (A) squared. 8 squared is 64 and 41664 divided by 64 is 651. Therefore, B equals 651.

Once again we have A and B and can get our answer to 41664 in its simplest radical form as follows:

√41664 = A√B

√41664 = 8√651

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