Evaluate {root[5+2root6]}+{root[8-2root15]}

Question : Evaluate {√[5+2√6]}+{√[8-2√15]}

Doubt by Bhumika

Solution :
 

= {√[5+2√6]}+{√[8-2√15]}
= {√[3+2+2√6]}+{√[5+3-2√15]}
= {√[(√3)²+(√2)²+2√3.√2]}+{√[(√5)²+(√3)²-2√5.√3]}

= {√[√3+√2]²}+{√[√5-√3]²}
[∵ Using Identities
a²+b²+2ab=(a+b)²
a²+b²-2ab=(a-b)² ]

= {√3+√2}+{√5-√3}
= √3+√2+√5-√3
= √2+√5