options: Represent and model with vector quantities.

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

Perform operations on matrices and use matrices in applications.

Extend the properties of exponents to rational exponents.

Use properties of rational and irrational numbers.

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

Reason quantitatively and use units to solve problems.

Perform arithmetic operations with complex numbers.

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

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

Perform operations on vectors.

Represent complex numbers and their operations on the complex plane.

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

Use complex numbers in polynomial identities and equations.
problem_activity: Task
Jessica evaluates $\sqrt{2}$ on her calculator which shows a value of
$$
1.4142136.
$$
She then writes
$$
\sqrt{2} = 1.4142136.
$$
Is Jessica correct?  Explain.
Explain, in terms of the structure of the expression $(1.4142136)^2$, why
it can not be equal to $2$.
Use the reasoning of part (b) to explain why $\sqrt{2}$ can not be equal
to any terminating decimal.


correct_option_index: 1

4