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 $(D)$