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

Let $$\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+................\infty}}}}=a$$

$$\Rightarrow$$ $$\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+..........\infty}}}}}=a$$

$$\Rightarrow$$ $$\sqrt{30+a}=a$$

$$\Rightarrow$$ $$30+a=a^2$$

$$\Rightarrow$$ $$a^2-a-30=0$$

$$\Rightarrow$$ $$a^2-6a+5a-30=0$$

$$\Rightarrow$$ $$a\left(a-6\right)+5\left(a-6\right)=0$$

$$\Rightarrow$$ $$\left(a-6\right)\left(a+5\right)=0$$

$$\Rightarrow$$ $$a-6=0$$   or   $$a+5=0$$

$$\Rightarrow$$  $$a=6$$    or   $$a=-5$$

$$a$$ cannot be negative

$$\Rightarrow$$  $$a=6$$

$$\therefore\ $$ $$\sqrt{30+\sqrt{30+\sqrt{30+\sqrt{30+................\infty}}}}=6$$

Hence, the correct answer is Option B