find which of the following number is a perfect square a) 19872
Answers
Answer:
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19872 to simplify the square root of 19872. 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 19872. The factors of 19872 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 32, 36, 46, 48, 54, 69, 72, 92, 96, 108, 138, 144, 184, 207, 216, 276, 288, 368, 414, 432, 552, 621, 736, 828, 864, 1104, 1242, 1656, 2208, 2484, 3312, 4968, 6624, 9936, and 19872. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.
B = Calculate 19872 divided by the greatest perfect square from the list of all factors of 19872. We determined above that the greatest perfect square from the list of all factors of 19872 is 144. Furthermore, 19872 divided by 144 is 138, therefore B equals 138.
Now we have A and B and can get our answer to 19872 in its simplest radical form as follows:
√19872 = A√B
√19872 = 12√138
Answer:
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 19872 to simplify the square root of 19872. 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 19872. The factors of 19872 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 32, 36, 46, 48, 54, 69, 72, 92, 96, 108, 138, 144, 184, 207, 216, 276, 288, 368, 414, 432, 552, 621, 736, 828, 864, 1104, 1242, 1656, 2208, 2484, 3312, 4968, 6624, 9936, and 19872. Furthermore, the greatest perfect square on this list is 144 and the square root of 144 is 12. Therefore, A equals 12.
B = Calculate 19872 divided by the greatest perfect square from the list of all factors of 19872. We determined above that the greatest perfect square from the list of all factors of 19872 is 144. Furthermore, 19872 divided by 144 is 138, therefore B equals 138.
Now we have A and B and can get our answer to 19872 in its simplest radical form as follows:
√19872 = A√B
√19872 = 12√138