Algebra Skills Refresher

Overview

• This unit focuses on reinforcing algebra skills between Algebra 1 and Algebra 2.
• Videos will highlight homework problems and offer worked examples.
• Additional examples and mastery quizzes are available for practice.

Topic: Radicals and Roots

• Radicals refer to square roots and cube roots.
  • Square root symbol often doesn't show the index (2), similar to not showing 1 in front of variables.
  • Opposite operations:
    • Squaring ↔ Square rooting
    • Cubing ↔ Cube rooting
  • Goal: Simplify by extracting perfect squares.

Simplification Process

1. Identify Perfect Squares:

   • Know squares of numbers: 1, 4, 9, 16, 25, etc.
   • Recommended to learn squares up to 15 for efficiency in factoring.

2. Factor the Number:

   • Example: Factor 392
     • 392 is even, so divide by 2 = 196
     • 196 is a perfect square (14x14)
     • Alternatively, factor 196 further:
       • 196: even, divide by 2 = 98
       • 98: even, divide by 2 = 49
       • 49 is a perfect square (7x7)

3. Rewrite in Terms of Perfect Squares:

   • Group factors as perfect squares.
   • Example: 392 = 2² x 7²
   • For variables: Break down using exponents
     • X³ = X² x X
     • Y² is already a perfect square
     • Z⁴ = Z² x Z²

4. Extract and Multiply:

   • Operate between the coefficient and radical as multiplication.
   • Move perfect squares out of the radical.
   • Example Operations:
     • ( \sqrt{2²} = 2 ) (comes out)
     • Remaining 2 stays under the radical
     • ( \sqrt{7²} = 7 ), ( \sqrt{X²} = X )
     • Remaining X, Y variables under radical if not perfect squared

5. Final Result:

   • Multiply extracted numbers/variables: 70 X Y Z²
   • Leave non-perfect squares under the radical as the exact answer.