Answer:
[tex]\displaystyle \frac{2}{7}+\sqrt{121}[/tex]
Step-by-step explanation:
Rational Numbers
A rational number is any number that can be expressed as a fraction
[tex]\displaystyle \frac{a}{b}, \ b\neq 0[/tex]
for a and b any integer and b different from 0.
As a consequence, any number that cannot be expressed as a fraction or rational number is defined as an Irrational number.
Let's analyze each one of the given options
[tex]\displaystyle \frac{5}{9}+\sqrt{18}[/tex]
The first part of the number is indeed a rational number, but the second part is a square root whose result cannot be expressed as a rational, thus the number is not rational
[tex]\pi + \sqrt{16}[/tex]
The second part is an exact square root (resulting 4) but the first part is a known irrational number called pi. It's not possible to express pi as a fraction, thus the number is irrational
[tex]\displaystyle \frac{2}{7}+\sqrt{121}[/tex]
The square root of 121 is 11. It makes the whole number a sum of a rational number plus an integer, thus the given number is rational
[tex]\displaystyle \frac{3}{10}+\sqrt{11}[/tex]
As with the first number, the square root is not exact. The sum of a rational number plus an irrational number gives an irrational number.
Correct option:
[tex]\boxed{\displaystyle \frac{2}{7}+\sqrt{121}}[/tex]
