Question

Can I add $2\sqrt{3} + 5\sqrt{3}$ further?

Answer 1

Yes, they can be added and simplified further. 2√3 + 5√3 = 7√3 .

Take √3 as common factor:

2√3 + 5√3

(2 + 5)√3

7√3

The two irrational numbers sums to form another irrational number 7√3 . In decimals that is 12.12435...

Answer 2

$\sf{\qquad\qquad\huge\underline{{\sf Answer}}}$

Yes, The terms assigned above are alike so they can be added easily by simple algebric method where root number can be treated as a variable.

$\qquad \sf  \dashrightarrow \: 2 \sqrt{3} + 5 \sqrt{3}$

$\qquad \sf  \dashrightarrow \: (2 + 5) \sqrt{3}$

$\qquad \sf  \dashrightarrow \: 7 \sqrt{3}$