Simplify Square Root of 94320

Here we will show you two methods that you can use to simplify the square root of 94320. In other words, we will show you how to find the square root of 94320 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.

√94320 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 94320 to simplify the square root of 94320. 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 94320. The factors of 94320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 131, 144, 180, 240, 262, 360, 393, 524, 655, 720, 786, 1048, 1179, 1310, 1572, 1965, 2096, 2358, 2620, 3144, 3930, 4716, 5240, 5895, 6288, 7860, 9432, 10480, 11790, 15720, 18864, 23580, 31440, 47160, and 94320. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Calculate 94320 divided by the greatest perfect square from the list of all factors of 94320. We determined above that the greatest perfect square from the list of all factors of 94320 is 144. Furthermore, 94320 divided by 144 is 655, therefore B equals 655.

Now we have A and B and can get our answer to 94320 in its simplest radical form as follows:

√94320 = A√B

√94320 = 12√655

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 94320 to simplify the square root of 94320 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 94320 and then take the square root of that product. The prime factors that multiply together to make 94320 are 2 x 2 x 2 x 2 x 3 x 3 x 5 x 131. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 3 x 3 = 144 and the square root of 144 is 12. Therefore, A equals 12.

B = Divide 94320 by the number (A) squared. 12 squared is 144 and 94320 divided by 144 is 655. Therefore, B equals 655.

Once again we have A and B and can get our answer to 94320 in its simplest radical form as follows:

√94320 = A√B

√94320 = 12√655

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