Question 202103



a) *[Tex \LARGE 3^{\frac{1}{2}}+2i] is <font color=red>complex</font> (ie not real) since there is an imaginary "i" term



b) {{{3.14}}} is <font color=red>real and rational</font> (assuming that it terminates) since {{{3.14=314/100=157/50}}}



c) {{{pi}}} is <font color=red>real and irrational</font> since this value is approximately 3.14159265... (and it doesn't terminate or have any repeating patterns)



d) *[Tex \LARGE 16^{\frac{1}{4}}+6=\sqrt[4]{16}+6=2+6=8] is <font color=red>real and rational</font> since {{{8=8/1}}}



e) *[Tex \LARGE 18^{\frac{1}{3}}] is <font color=red>real and irrational</font> (since it cannot be represented as a fraction of whole numbers)



f) {{{1/6}}} is <font color=red>real and rational</font> (since it is a "ratio" of whole numbers)



g) {{{6i}}} is <font color=red>complex</font> (ie not real) since there is an imaginary "i" term



h) *[Tex \LARGE 3-\left(-9\right)^{\frac{1}{2}}=3-\sqrt{-9}=3-3i] is <font color=red>complex</font> (ie not real) since there is an imaginary "i" term




Note: if a number is either rational or irrational, it is automatically real.