d,
$\dfrac{\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{6}+\sqrt[]{8}+\sqrt[]16}{\sqrt[]2+\sqrt[]3+\sqrt[]4}=\dfrac{\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{6}+\sqrt[]{8}+4}{\sqrt[]2+\sqrt[]3+\sqrt[]4}=\dfrac{(\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{4})+(\sqrt[]{4}+\sqrt[]{6}+\sqrt[]{8})}{\sqrt[]2+\sqrt[]3+\sqrt[]4}=\dfrac{(\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{4})+\sqrt[]{2}(\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{4})}{\sqrt[]2+\sqrt[]3+\sqrt[]4}=\dfrac{(\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{4})(1+\sqrt[]2)}{\sqrt[]2+\sqrt[]3+\sqrt[]4}=1+\sqrt[]2$
