#### Math - 2018-19

# AII.1b - Radical Expressions

AII.1The student willb)

add,subtract,multiply,divide, andsimplifyradical expressions containing rational numbers and variables, and expressions containing rational exponents;

*Adopted: 2016*

### BIG IDEAS

- I can design the track of a
roller coaster, determine the sloped curve of an exit ramp, trace the free
falling path of a skydiver, and
understand the mechanics of controllers like
autopilot, cruise control, and a living room thermostat.

- I will
apply mathematical processes for basic operations to algebraic expressions and
divide algebraic terms out of algebraic expressions.

### UNDERSTANDING THE STANDARD

· Computational skills applicable to numerical fractions also apply to rational expressions involving variables.

· Radical expressions can be written and simplified using rational exponents.

· Only radicals with a common radicand and index can be added or subtracted, which may require rewriting a radical with a lower base and different index.

· A relationship exists among arithmetic complex fractions, algebraic complex fractions, and rational numbers.

· The complete factorization of polynomials has occurred when each factor is a prime polynomial.

· Pattern recognition can be used to determine complete factorization of a polynomial.

· Polynomials may be factored in various ways, including, but not limited to grouping or applying general patterns such as difference of squares, sum and difference of cubes, and perfect square trinomials.

### ESSENTIALS

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

·
AII.1b_{1} **Simplify**
radical expressions containing positive rational numbers and variables.

·
AII.1b_{2} **Convert**
between radical expressions and expressions containing rational exponents.

·
AII.1b_{3} **Add**
and **subtract** radical expressions.

· AII.1b_{4} **Multiply**
and **divide** radical expressions.
Simplification may include rationalizing denominators.

### KEY VOCABULARY

rational,
radical, polynomial expression, simplify, variables, equation vs. expression,
factor completely, rational exponents,
sum, difference,product,
quotient,monomial, binomial,
complex algebraic fraction, simple algebraic fraction, radical expression,
radical notation, exponential notation, rationalizing, numerator, denominator,
difference of squares, difference of cubes, sum of cubes, perfect square
trinomial, integer, verify

*Updated: Aug 23, 2018*