Simplify Square Root of 98496

Here we will show you two methods that you can use to simplify the square root of 98496. In other words, we will show you how to find the square root of 98496 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.

√98496 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 98496 to simplify the square root of 98496. 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 98496. The factors of 98496 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38, 48, 54, 57, 64, 72, 76, 81, 96, 108, 114, 144, 152, 162, 171, 192, 216, 228, 288, 304, 324, 342, 432, 456, 513, 576, 608, 648, 684, 864, 912, 1026, 1216, 1296, 1368, 1539, 1728, 1824, 2052, 2592, 2736, 3078, 3648, 4104, 5184, 5472, 6156, 8208, 10944, 12312, 16416, 24624, 32832, 49248, and 98496. Furthermore, the greatest perfect square on this list is 5184 and the square root of 5184 is 72. Therefore, A equals 72.

B = Calculate 98496 divided by the greatest perfect square from the list of all factors of 98496. We determined above that the greatest perfect square from the list of all factors of 98496 is 5184. Furthermore, 98496 divided by 5184 is 19, therefore B equals 19.

Now we have A and B and can get our answer to 98496 in its simplest radical form as follows:

√98496 = A√B

√98496 = 72√19

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 98496 to simplify the square root of 98496 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 98496 and then take the square root of that product. The prime factors that multiply together to make 98496 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 19. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 = 5184 and the square root of 5184 is 72. Therefore, A equals 72.

B = Divide 98496 by the number (A) squared. 72 squared is 5184 and 98496 divided by 5184 is 19. Therefore, B equals 19.

Once again we have A and B and can get our answer to 98496 in its simplest radical form as follows:

√98496 = A√B

√98496 = 72√19

Simplify Square Root
Please enter another square root in the box below for us to simplify.

Simplify Square Root of 98497
Here is the next square root on our list that we have simplifed for you.