Simplify Square Root of 19360

Here we will show you two methods that you can use to simplify the square root of 19360. In other words, we will show you how to find the square root of 19360 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.

√19360 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19360 to simplify the square root of 19360. 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 19360. The factors of 19360 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 80, 88, 110, 121, 160, 176, 220, 242, 352, 440, 484, 605, 880, 968, 1210, 1760, 1936, 2420, 3872, 4840, 9680, and 19360. Furthermore, the greatest perfect square on this list is 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Calculate 19360 divided by the greatest perfect square from the list of all factors of 19360. We determined above that the greatest perfect square from the list of all factors of 19360 is 1936. Furthermore, 19360 divided by 1936 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 19360 in its simplest radical form as follows:

√19360 = A√B

√19360 = 44√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 19360 to simplify the square root of 19360 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 19360 and then take the square root of that product. The prime factors that multiply together to make 19360 are 2 x 2 x 2 x 2 x 2 x 5 x 11 x 11. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 11 x 11 = 1936 and the square root of 1936 is 44. Therefore, A equals 44.

B = Divide 19360 by the number (A) squared. 44 squared is 1936 and 19360 divided by 1936 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 19360 in its simplest radical form as follows:

√19360 = A√B

√19360 = 44√10

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