Consider the first radical :
[tex]{:\implies \quad \sf 5\times 2\dfrac16}[/tex]
Using the properties of mixed fraction, writing the mixed fraction as an improper fraction, we will be having
[tex]{:\implies \quad \sf 5\times \bigg(\dfrac{6\times 2+1}{6}\bigg)}[/tex]
[tex]{:\implies \quad \sf 5\times \bigg(\dfrac{12+1}{6}\bigg)}[/tex]
[tex]{:\implies \quad \sf 5\times \dfrac{13}{6}}[/tex]
[tex]{:\implies \quad \sf \dfrac{65}{6}}[/tex]
[tex]{:\implies \quad \boxed{\bf{10\dfrac56}}}[/tex]
Hence, Option D) is correct
Now, coming to the 2nd question :
[tex]{:\implies \quad \sf 3\dfrac{1}{2}\times 1\dfrac{2}{3}}[/tex]
[tex]{:\implies \quad \sf \bigg(\dfrac{3\times 2+1}{2}\bigg)\times \bigg(\dfrac{3\times 1+2}{3}\bigg)}[/tex]
[tex]{:\implies \quad \sf \bigg(\dfrac{6+1}{2}\bigg)\times \bigg(\dfrac{3+2}{3}\bigg)}[/tex]
[tex]{:\implies \quad \sf \dfrac{7}{2}\times \dfrac{5}{3}}[/tex]
[tex]{:\implies \quad \sf \dfrac{35}{6}}[/tex]
Now, Rewriting this improper fraction as mixed fraction, we will be having :
[tex]{:\implies \quad \boxed{\bf{5\dfrac56}}}[/tex]
Hence, Option C) is correct
