which expression represents a rational number?\n$\frac{5}{9}+sqrt{18}$\n$pi+sqrt{16}$\n$\frac{2}{7}+sqrt{121}…

Explanation:

Step1: Recall the definition of rational and irrational numbers

A rational number can be written as a fraction $\frac{a}{b}$ where $a,b$ are integers and $b\neq0$. An irrational number cannot be written as a fraction. $\sqrt{n}$ is rational if $n$ is a perfect - square and irrational if $n$ is not a perfect - square, and $\pi$ is irrational.

Step2: Analyze each option

Option 1: $\frac{5}{9}+\sqrt{18}$

Since $\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$, and $\sqrt{2}$ is irrational, $\frac{5}{9}+\sqrt{18}$ is irrational.

Option 2: $\pi+\sqrt{16}$

Since $\pi$ is irrational and $\sqrt{16} = 4$, $\pi+\sqrt{16}$ is irrational.

Option 3: $\frac{2}{7}+\sqrt{121}$

Since $\sqrt{121}=11$, then $\frac{2}{7}+\sqrt{121}=\frac{2}{7}+11=\frac{2 + 77}{7}=\frac{79}{7}$, which is a rational number.

Option 4: $\frac{3}{10}+\sqrt{11}$

Since $\sqrt{11}$ is irrational, $\frac{3}{10}+\sqrt{11}$ is irrational.

Answer:

$\frac{2}{7}+\sqrt{121}$