PK 2018 Q16
16. In the calculation shown, how many times does the term \(2018^2\) appear inside the square root to make the calculation correct?
\(\sqrt{2018^2 + 2018^2 + \ldots + 2018^2} = 2018^{10}\)
- A 5
- B 8
- C 18
- D \(2018^8\)
- E \(2018^{18}\)
Pink Kangaroo 2018, Question 16. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E \(2018^{18}\)
Square both sides to get \(2018^2 + 2018^2 + \ldots + 2018^2 = 2018^{20}\).
Let \(n\) be the number of occurrences of \(2018^2\). Then we get \(2018^2 \times n = 2018^{20}\).
So \(n = \dfrac{2018^{20}}{2018^2} = 2018^{18}\).
Solution © UK Mathematics Trust, from the PK 2018 solutions.