#### Math - 2017-18

# AII.1c - Radical Expressions

The student, given rational, radical, or polynomial expressions, will

c) **write **radical
expressions as expressions containing rational exponents and vice versa;

**Bloom's Level:** Apply

*Adopted: 2009*

### 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.
- 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.

### ESSENTIALS

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

All.1c_{1} **Convert **from radical
notation to exponential notation, and vice versa. **Solve **an equation containing a radical expression.

### 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: Feb 07, 2018*