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

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To simplify (√3 + 2√5)², first apply the FOIL method, resulting in (√3)² + 2(√3)(2√5) + (2√5)². This expands to 3 + 4√15 + 20. Combining the constant terms gives a final result of 23 + 4√15. The step-by-step approach effectively demonstrates the simplification process.
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How?

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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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