Question

What much expression represents a rational number?

Answer 1

Answer:

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

Step-by-step explanation:

Rational Numbers

A rational number is any number that can be expressed as a fraction

$\displaystyle \frac{a}{b}, \ b\neq 0$

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

$\displaystyle \frac{5}{9}+\sqrt{18}$

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

$\pi + \sqrt{16}$

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

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

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

$\displaystyle \frac{3}{10}+\sqrt{11}$

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:

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