# AII.1b and *AII.1b - Radical Expressions

AII.1    The student, given rational, radical, or polynomial expressions, will

b)  add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents;

AII.1  The student will

b) add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents;

Bloom's Level:  Apply

### 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.
• 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.

·  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

Simplifying

All.1b1  Simplify radical expressions containing positive rational numbers and variables.

·  AII.1b1  Simplify radical expressions containing positive rational numbers and variables.

Convert to Exponents

All.1c1  Convert from radical notation to exponential notation, and vice versa.  Solve an equation containing a radical expression.

·  AII.1b2  Convert between radical expressions and expressions containing rational exponents.

Operations