Problem 7 · 2021 Math Kangaroo
Medium
Algebra & Patterns
substitution
Let \(x = \tfrac{\pi}{4}\). Which of the following numbers is the largest?
Show answer
Answer: E — \(\sqrt[4]{x}\)
Show hints
Hint 1 of 2
Notice x = π/4 is less than 1.
Still stuck? Show hint 2 →
Hint 2 of 2
For a number between 0 and 1, decide whether higher or lower powers give a larger value.
Show solution
Approach: compare powers of a number below 1
- x = π/4 ≈ 0.785, which is between 0 and 1.
- For such x, raising to a higher power makes it smaller, while taking a root makes it larger.
- The largest value comes from the smallest exponent, the fourth root: ∜x.
Mark:
· log in to save