How to simplify (√3 + 2√5)²

[pan90]

How?

View attachment 9222

Taken from HiSet free practice test

 

[topsquark]

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