Chapter 1.3, Problem 49ES

The Four 4s Problem The object at this exercise is to create mathematical expressions that use exactly four 4s and that simplify to a counting number from 1 to 20, inclusive. You are allowed to use the following mathematical symbols: $+,-,\times ,÷,\sqrt{},\left(,and\right)$. For example,

$\frac{4}{4}+\frac{4}{4}=2,4^{\left(4-4\right)}+4=5$

$4-\sqrt{4}+4\times 4=18$