Simplifying Radicals with Mario's Math Tutoring

Introduction

• The goal is to simplify radicals in a less stressful way.
• Traditional methods involve dividing by perfect squares (4, 9, 16, 25).
• This method can be challenging for students with weak multiplication skills or when dealing with large numbers.

Prime Factorization Method

• Step 1: Perform a prime factorization of the number.
  • Example: 48 becomes 8 x 6, 8 becomes 4 x 2, 4 becomes 2 x 2, 6 becomes 3 x 2.
  • Break down the number until only prime numbers are left.
• Step 2: Look for pairs or groups of numbers depending on the root.
  • Square Root: Look for pairs (two of the same number).
  • Cube Root: Look for triplets (three of the same number).
  • Fourth Root: Look for quadruplets (four of the same number).
• Step 3: Group numbers accordingly.
  • Example: For square roots, each pair contributes one number outside the square root.

Examples

• Square Root of 48:

  • Prime factorization: 48 = 2 x 2 x 2 x 2 x 3.
  • Pairs: 2 x 2 = 4 (square root is 2).
  • Simplified form: 4√3.
  • Verification: 4² x 3 = 48.

• Square Root of 72:

  • Prime factorization: 72 = 2 x 2 x 2 x 3 x 3.
  • Pairs: Two pairs of 2s and one pair of 3s.
  • Simplified form: 6√2.
  • Calculation: (2 x 3)√2 = 6√2.

• Cube Root of 96:

  • Prime factorization: 96 = 2 x 2 x 2 x 2 x 2 x 3.
  • Group: Three 2s form a group.
  • Simplified form: 2 x cube root of 12.
  • Remaining factors: 2 x 2 x 3 = 12 inside the cube root.

Key Takeaways

• Use prime factorization to simplify radicals effectively.
• Identify and group prime factors to simplify calculations.
• Practice breaking down numbers and forming appropriate groups for different roots.

Conclusion

• Simplifying radicals through prime factorization is an effective technique.
• Encouraged to subscribe to the channel for more tips.
• Look forward to future math videos for additional learning.