Verified answer

let √(30+√(30+........ =x

then consider √(30+x)=x

squaring on both sides

30+x=x^2

then by rearranging the terms we get

x^2-x-30=0

x^2-(6-5)x-30=0

as -x can be written as -6x and +5x and also (-6)(5)=-30 which gives u product

the above process is just normal factorization

the equation becomes

x^2-6x+5x-30=0

x(x-6)+5(x-6)=0

(x-6)(x+5)=0

so x=6 or -5

but firstly we have assumed √30+V(30+,........=x

so x cannot be negative

hence the answer is 6

Let x=√(30+√(30+√(30+...))))

x = √30+x --- square root of (30+x)

square both sides

x^2 = (30+x)

x^2-x-30=0

(x-6)(x+5)=0

x=6 or x=-5