Simplify Square Root of 98112

Here we will show you two methods that you can use to simplify the square root of 98112. In other words, we will show you how to find the square root of 98112 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.

√98112 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 98112 to simplify the square root of 98112. 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 98112. The factors of 98112 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 73, 84, 96, 112, 146, 168, 192, 219, 224, 292, 336, 438, 448, 511, 584, 672, 876, 1022, 1168, 1344, 1533, 1752, 2044, 2336, 3066, 3504, 4088, 4672, 6132, 7008, 8176, 12264, 14016, 16352, 24528, 32704, 49056, and 98112. Furthermore, the greatest perfect square on this list is 64 and the square root of 64 is 8. Therefore, A equals 8.

B = Calculate 98112 divided by the greatest perfect square from the list of all factors of 98112. We determined above that the greatest perfect square from the list of all factors of 98112 is 64. Furthermore, 98112 divided by 64 is 1533, therefore B equals 1533.

Now we have A and B and can get our answer to 98112 in its simplest radical form as follows:

√98112 = A√B

√98112 = 8√1533

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 98112 to simplify the square root of 98112 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 98112 and then take the square root of that product. The prime factors that multiply together to make 98112 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 73. 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 98112 by the number (A) squared. 8 squared is 64 and 98112 divided by 64 is 1533. Therefore, B equals 1533.

Once again we have A and B and can get our answer to 98112 in its simplest radical form as follows:

√98112 = A√B

√98112 = 8√1533

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