Using the numbers 5, 8, and 24, create a problem using no more than four operations (addition, subtraction, multiplication, divi
sion, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your operations is an irrational number.
There could be many answers to this problem, one being the √(24 x 5 - 8)
Step-by-step explanation:
Irrational numbers are classified as real numbers that are non-terminating and non-repeating decimals. This means that the number will be a decimal that never ends and does not contain a pattern of any kind. For example, a decimal that never ends is usually written as: 5.6789234... This type of number is irrational because the decimal keeps going and shows no pattern of repetition. In the answer given, the value of (24 x 5 -8) is 112. The square root of 112 is not a perfect square and thus you will get a non-terminating and non-repeated decimal as the final answer, thus making it irrational.
The horizontal stretch is the correct answer. A period is the distance on the x-axis that it takes for the tangent or cotangent function to repeat itself. Stretching it out horizontally will lengthen that distance and therefore change the period.
