x=√(√6+√6+√6+….)

Question

find the value of x

Answer 1

x^2=(√6+√6+√6+….)

or,x^4 = 6 +(√6+√6+√6+….)      {Squaring both side we have this}

or,x^4 - 6 = (√6+√6+√6+….)

As We Know,x^2=(√6+√6+√6+….)

So, x^4 - 6 = x^2

or,x^4 - x^2 - 6 = 0

or,(x^2+2)(x^2-3) = 0

or,x^2 = 3
or,x=root(3)