Simplify (√3 + 2√5)²: Step-by-Step Guide

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SUMMARY

The discussion focuses on simplifying the expression (√3 + 2√5)² using the FOIL method. The initial steps include expanding the expression to (√3)² + √3·2√5 + 2√5·√3 + (2√5)². The final result of the simplification is 3 + 4√15 + 20, leading to the complete expression of 23 + 4√15. This method effectively demonstrates the application of the FOIL technique in algebraic expansion.

PREREQUISITES
  • Understanding of the FOIL method for binomial expansion
  • Knowledge of square roots and their properties
  • Basic algebraic manipulation skills
  • Familiarity with simplifying radical expressions
NEXT STEPS
  • Practice additional problems using the FOIL method for different binomials
  • Explore the properties of square roots and their simplifications
  • Learn about polynomial expansion techniques beyond FOIL
  • Study the application of radical expressions in real-world scenarios
USEFUL FOR

Students preparing for standardized tests, educators teaching algebra, and anyone looking to strengthen their understanding of binomial expansion and radical simplification.

pan90
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How?

View attachment 9222

Taken from HiSet free practice test
 

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pan90 said:
How?
Taken from HiSet free practice test
FOIL it out:
[math]( \sqrt{3} + 2 \sqrt{5} ) ^2 = ( \sqrt{3} + 2 \sqrt{5} ) ( \sqrt{3} + 2 \sqrt{5} )[/math]

[math]= ( \sqrt{3} )^2 + \sqrt{3} \cdot 2 \sqrt{5} + 2 \sqrt{5} \cdot \sqrt{3} + (2 \sqrt{5} )^2[/math]

Can you finish from here?

-Dan
 

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