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.

$\begin{gathered} \frac{x}{y} \\ \text{where} \\ y\ne0 \end{gathered}$

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.

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

c.

$\begin{gathered} \sqrt[]{6}\times23=23\sqrt[]{6} \\ The\text{ product of the irrational number(}\sqrt[]{6}\text{) and rational number(23) will result in an irrational number.} \end{gathered}$

d.

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