Question Number 129663 by liberty last updated on 17/Jan/21
$$\:\sqrt{\mathrm{14}+\sqrt{\mathrm{3}}\:+\sqrt[{\mathrm{3}}]{\mathrm{26}−\mathrm{5}\sqrt{\mathrm{3}}}}\:=?\: \\ $$
Commented by MathSh last updated on 17/Jan/21
$$\sqrt[{\mathrm{3}}]{\left(\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }=\sqrt[{\mathrm{3}}]{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }=\mathrm{2}−\sqrt{\mathrm{3}} \\ $$$$\sqrt{\mathrm{14}+\sqrt{\mathrm{3}}+\mathrm{2}−\sqrt{\mathrm{3}}}=\sqrt{\mathrm{16}}=\mathrm{4} \\ $$
Commented by liberty last updated on 17/Jan/21
$$\mathrm{wrong} \\ $$
Commented by liberty last updated on 17/Jan/21
Commented by MathSh last updated on 17/Jan/21
$${Yes},\:``−\mathrm{5}''\:{and}\:``−\mathrm{15}'' \\ $$