in the venn diagram, consider u = {whole numbers 1 - 100}. let a represent numbers that are perfect squares…
in the venn diagram, consider u = {whole numbers 1 - 100}. let a represent numbers that are perfect squares, b represent numbers that are perfect cubes, and c represent numbers that are perfect fourths, or numbers with a fourth root that is an integer. which number(s) satisfy a ∩ c? 16, 81 1, 16, 81 1, 4, 9, 16, 25, 36, 49, 81, 100 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Answer
Answer:
1, 16, 81
Explanation:
Step1: List perfect - squares
The perfect squares from 1 to 100 are $n^2$ where $n = 1,2,\cdots,10$. So $A={1,4,9,16,25,36,49,64,81,100}$.
Step2: List perfect - fourths
The perfect fourths from 1 to 100 are $m^4$ where $m = 1,2,3$. So $C = {1,16,81}$.
Step3: Find the intersection
The intersection $A\cap C$ consists of elements that are in both $A$ and $C$. So $A\cap C={1,16,81}$.