The value of \(\sqrt {103+20\sqrt {3 }}\) - \(\sqrt {7-4\sqrt {3 }}\) is closest to:

13.4 11.4 11.9 10.6

11.4

103 - 20\(\sqrt {3}\) can be written as \( {(10+\sqrt {3}})^{2}\) and 7 - 4\(\sqrt {3}\) can be written as \( {(2-\sqrt {3}})^{2}\) So, Put in question ⇒ \(\sqrt {{(10+\sqrt {3}})^{2}}\) - \(\sqrt {{(2-\sqrt {3}})^{2}}\) ⇒ 10+\(\sqrt {3}\) - 2 + \(\sqrt {3}\) ⇒ 8 + 2\(\sqrt {3}\) = 11.4