standard_description: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
problem_activity: Task
In each of the following problems, a number is given. If possible, determine whether the given number is rational or irrational. In some cases, it may be impossible to determine whether the given number is rational or irrational. Justify your answers.
$ 4 + \sqrt{7} $
$ \displaystyle \frac{\sqrt{45}}{\sqrt{5}} $
$ \displaystyle \frac{6}{\pi} $
$ \sqrt{2} + \sqrt{3} $
$ \displaystyle \frac{2 + \sqrt{7}}{2a + \sqrt{7a^2}}$, where $a$ is a positive integer
$ x + y$, where $x$ and $y$ are irrational numbers


aligns: no