Quandaries
and Queries
Hi
My name is linda and I am a teacher having difficulties in solving the following question: Which number is greater 3111 or 1714 (without using calculator). Thanks for your help.
Linda,
Perhaps before taking the powers you are intended to replace 31 by the slightly larger 25, and replace 17 by the slightly smaller 24.
Chris
Linda:
The key to this problem is 17
2 = 34 and 34 > 31.
3111 < 3411
3411 = (17x2)11 = (1711) x (211) = 1711 x 24 x 24 x 23
1711 x 24 x 24 x 23 < 1711 x 17 x 17 x 17
1711 x 17 x 17 x 17 = 1714
Therefore, 3111 < 1714
Paul