The expression $\sqrt{13+3\sqrt{\frac{23}{3}}} +\sqrt{13-3\sqrt{\frac{23}{3}}} $ is which type of number? 
(a) A natural number,
(b) A rational number but not a natural number,
(c) An irrational number not exceeding 6,
(d) An irrational number
exceeding 6.

Please help with this, i can't manage to simplify it. Thanks in advance.

Let us assume 
$$\sqrt{13+3\sqrt{\frac{23}{3}}} +\sqrt{13-3\sqrt{\frac{23}{3}}}=x $$
Squaring and simplifying  gives 
 $$26+20=x^2$$
which gives $$x=+\sqrt{46}$$
Since $6=
\sqrt{36}<\sqrt{46}<\sqrt{49}=7$
The result is $(D)$
