underroot of (11+4(underoot7))?....how this ends up to (2+underoot7)??

Question

√(11+(2√7))=2+√7???

 

Answer 1

√(11+[4√7])=2+√7

square both sides and you will see that they are equal

however,...

√(11+[4√7])=

√(4+7+2√7+2√7)=

√(2²+2√7+2√7+7)=

(√7)²=7 and 2²=4

factor the radicand

√[(2+√7)(2+√7)]=

2+√7