a: \(=\sqrt{4}+\sqrt{9}-\sqrt{16}+\sqrt{105:\dfrac{15}{7}}\)
\(=2+3-4+\sqrt{105\cdot\dfrac{7}{15}}\)
=1+7=8
b: \(=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1+\sqrt{2}\)
\(\dfrac{\sqrt{20}}{\sqrt{5}}+\dfrac{\sqrt{117}}{\sqrt{13}}-\dfrac{\sqrt{272}}{\sqrt{17}}+\dfrac{\sqrt{105}}{\sqrt{2\dfrac{1}{7}}}\)
\(=\sqrt{\dfrac{20}{5}}+\sqrt{\dfrac{117}{13}}-\sqrt{\dfrac{272}{17}}+\sqrt{\dfrac{105}{\dfrac{15}{7}}}\)
\(=\sqrt{16}+\sqrt{9}-\sqrt{16}+\sqrt{49}\)
`=2+ 3 - 4 + 7`
`=8`
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\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+2}\)
\(=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\dfrac{\left[\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\left(\sqrt{4}+\sqrt{6}+\sqrt{8}\right)\right]}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\dfrac{\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)+\left(1+\sqrt{2}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=1+\sqrt{2}\)
