options: Compute fluently with multi-digit numbers and find common factors and multiples.

Perform operations on vectors.

Apply and extend previous understandings of numbers to the system of rational numbers.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Represent and model with vector quantities.

Perform arithmetic operations with complex numbers.

Reason quantitatively and use units to solve problems.

Use complex numbers in polynomial identities and equations.

Perform operations on matrices and use matrices in applications.

Extend the properties of exponents to rational exponents.

Use properties of rational and irrational numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Represent complex numbers and their operations on the complex plane.
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


correct_option_index: 10

11