Given the rational number:
![(590)/(160)](https://img.qammunity.org/2023/formulas/mathematics/college/hdyiaqx5ndwa4jiu597ay605k5i28oe8d3.png)
Given the square root:
![√(17)](https://img.qammunity.org/2023/formulas/mathematics/high-school/dn3avx1vj8vqn4dplojb9iyngfgvbwxc0a.png)
Let's determine if the rational number is a reasonable approximation for the square root.
A rational number is a number that can be expressed as a fraction or ratio of two numbers.
Now, let's first determine if the square root is a rational number.
![√(17)](https://img.qammunity.org/2023/formulas/mathematics/high-school/dn3avx1vj8vqn4dplojb9iyngfgvbwxc0a.png)
The square root is not a rational number.
Since it is not a rational number, it cannot be the approximation of any rational number.
Therefore, the rational number is NOT a reasonable approximation of the square root.
ANSWER: