Arrange the following numbers in descending orders of magnitude: 22three, 34five, 21six

Answer Details

To compare these numbers, we need to convert all of them to the same base. Let's convert them all to base 10 for simplicity: - 22_three = 2\*3¹ + 2\*3⁰ = 6 + 2 = 8 - 34_five = 3\*5¹ + 4\*5⁰ = 15 + 4 = 19 - 21_six = 2\*6¹ + 1\*6⁰ = 12 + 1 = 13 So, in base 10, the numbers are 8, 19, and 13. To arrange them in descending order of magnitude, we simply sort them from largest to smallest: - 19, 13, 8 Therefore, the correct answer is: 34_five, 21_six, 22_three