Simplify Square Root of 97416

Here we will show you two methods that you can use to simplify the square root of 97416. In other words, we will show you how to find the square root of 97416 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.

√97416 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97416 to simplify the square root of 97416. 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 97416. The factors of 97416 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 27, 33, 36, 41, 44, 54, 66, 72, 82, 88, 99, 108, 123, 132, 164, 198, 216, 246, 264, 297, 328, 369, 396, 451, 492, 594, 738, 792, 902, 984, 1107, 1188, 1353, 1476, 1804, 2214, 2376, 2706, 2952, 3608, 4059, 4428, 5412, 8118, 8856, 10824, 12177, 16236, 24354, 32472, 48708, and 97416. Furthermore, the greatest perfect square on this list is 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Calculate 97416 divided by the greatest perfect square from the list of all factors of 97416. We determined above that the greatest perfect square from the list of all factors of 97416 is 36. Furthermore, 97416 divided by 36 is 2706, therefore B equals 2706.

Now we have A and B and can get our answer to 97416 in its simplest radical form as follows:

√97416 = A√B

√97416 = 6√2706

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97416 to simplify the square root of 97416 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 97416 and then take the square root of that product. The prime factors that multiply together to make 97416 are 2 x 2 x 2 x 3 x 3 x 3 x 11 x 41. When we strip out the pairs only, we get 2 x 2 x 3 x 3 = 36 and the square root of 36 is 6. Therefore, A equals 6.

B = Divide 97416 by the number (A) squared. 6 squared is 36 and 97416 divided by 36 is 2706. Therefore, B equals 2706.

Once again we have A and B and can get our answer to 97416 in its simplest radical form as follows:

√97416 = A√B

√97416 = 6√2706

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