Radicals+quiz+3+review+key

Key Radicals - Quiz 3 Review

Page 1: Radical Expressions

1. Convert expressions to radical form:

   • Example: k° : LY 4K"

     • This expression needs proper context to convert precisely.

2. Convert expressions to rational exponent form:

   • Example: /5n

     • Apply the rules for fractional exponents according to property rules.

Simplification

3. Simplifying the expressions:

   • Expression: 3m'n - mn

     • Combine like terms using exponent rules.

   • Expression: ab² - a*b'

     • Apply exponents on both terms to simplify further.

   • Additional examples include:

     • 64°: Simplifies to 1, since any number to the power of zero is 1.

     • 277: Explanatory notes may be necessary.

     • Numerous numbers and expressions: Includes evaluating expressions such as 25x", 36h) and ensuring they are in simplest form without fractional exponents.

Key Exponents

4. Handling specific cases:

   • Always ensure answers contain only positive exponents and fractions are eliminated from the denominator where needed.

   • Example:

     • When working with roots, consider simplified radical forms or expressions.

Page 2: Equations and Inequalities

1. Solving equations and inequalities:

   • Ensure extraneous solutions are checked when solving each equation.

2. Example Problems:

   • Equation 14: 2 =./E-5- Further evaluation required to determine the solution.

   • Equation 15: 2 - n = -1 + √(3 - n)- Combine like terms and isolate n.

   • Equation 16: - (14a)* = 1- Solve for a through simplification methods.

   • Inequality 17: ¥5x + 10 - 5 = 9- Rearranging and simplifying needed.

   • Inequality 18: jax + 5 + 1 > 4- Combine terms to solve for x.

   • Inequality 19: 6 + \3By + 4 < 0- Solving the inequality requires isolating terms for analysis.