Correct option : (a) 3
\((28+10\sqrt3)^{1/2} =(25 +3+10\sqrt3)^\frac12\)
\(=(5^2+(\sqrt3)^2 +2\times 5\times \sqrt3)^\frac12\)
\(=((5+\sqrt3)^2)^\frac12 =5+\sqrt3.\)
Also, \((7-4\sqrt3)^{-1/2} =\frac{1}{(7-4\sqrt3)^\frac12}=\frac{1}{(4+3-4\sqrt3)^\frac12}\)
\(=\frac{1}{(2^2+(\sqrt3)^2-2 \times 2 \times \sqrt3)^\frac12}\)
\(=\frac{1}{((2-\sqrt3)^2)^\frac12} =\frac{1}{2-\sqrt3} =\frac{2+\sqrt3}{4-3} =2+\sqrt3\)
\(\therefore (28+10\sqrt3)^\frac12-(7-4\sqrt3)^{-1/2}\)
\(=(5+\sqrt3)-(2+\sqrt3) =3.\)
