Question

Result is Result isRational IrrationalReason(a) 34 +O(Choose one)12(b)4+ -21(Choose one)17(c) ſo6 x 23(Choose one)13(d)8 x(Choose one)19

Answer 1

Firstly, rational numbers are numbers that can be express in the form of a ratio.

`\begin{gathered} (x)/(y) \\ \text{where} \\ y\\e0 \end{gathered}`

Irrational numbers are numbers that cannot be express in the form of a fraction. These numbers are non-terminating. Therefore,

a.

`\begin{gathered} 34+\sqrt[]{7}=34+\sqrt[]{7} \\ 34\text{ is a rational number as it can be express in fraction} \\ \sqrt[]{7}\text{ is an irrational number. The square root of 7 is non-terminating.} \\ \text{The sum of a rational and an irrational number will }always\text{ be an irrational number} \end{gathered}`

b.

`\begin{gathered} (12)/(17)+(4)/(21)=(252+68)/(357)=(320)/(357)(rational) \\ \text{The sum of 2 rational numbers }produces\text{ a rational number.} \\ \text{Notice that the individual numbers can be express in fractions. This makes them rational.} \end{gathered}`

c.

d.

`\begin{gathered} 8*(13)/(19)=(104)/(19) \\ 8\text{ is rational number} \\ (13)/(19)\text{ is a rational number because it can be express in fraction.} \\ \text{The product of the 2 rational number will produce a rational number (}(104)/(19)\text{)} \end{gathered}`