Question

simplify
$\sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3 \sqrt{3} } } } }$
​

Answer 1

Explanation:

a=√3(√3(√3(√3(√3…….inf.))))

sq. both sides

a^2=3(√3(√3(√3(√3(√3…….inf.)))))

or

a^2=3a ; since, a=√3(√3(√3(√3(√3…….inf.))))

a^2-3a=0

a(a-3)=0

a=0/3

0 logically doesn't fit so 3 is the ans :)