Problem:
Find the smallest positive number from the numbers below.
Answer Choices:
A. 10−311​
B. 311​−10
C. 18−513​
D. 51−1026​
E. 1026​−51
Solution:
Since 102=100>99=(311​)2,
​182=324<325=(513​)2,512=2601>2600=(1026​)2,​
only (A) and (D) are positive numbers.
Moreover, since a−b=a+ba2−b2​, 10−311​=10+311​1​≈201​ and 51−1026​=51+1026​1​≈1021​.
So (D) is the answer.