Find the value of $\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+.................∞}}}}$

6

$\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+.................∞}}}}$

In this type of question when there is plus sign in the equation and we have to find the value of the given equation then we will do prime factorization of the number given in the equation and choose largest factor of the factors as given below,

The prime factorization of the given equation = 30 = 6 × 5

So the value of $\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+.................∞}}}}$ = 6