options: Represent complex numbers and their operations on the complex plane.

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

Extend the properties of exponents to rational exponents.

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

Reason quantitatively and use units to solve problems.

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

Perform operations on matrices and use matrices in applications.

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

Use complex numbers in polynomial identities and equations.

Perform arithmetic operations with complex numbers.

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

Represent and model with vector quantities.

Perform operations on vectors.

Use properties of rational and irrational numbers.
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: 2

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