14-3-26-5-3-1-3-

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

(((26−15(√3))^3 ))^(1/3) =(((2−(√3))^3 ))^(1/3) =2−(√3) (√(14+(√3)+2−(√3)))=(√(16))=4

$$\sqrt[{\mathrm{3}}]{\left(\mathrm{26}−\mathrm{15}\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }=\sqrt[{\mathrm{3}}]{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }=\mathrm{2}−\sqrt{\mathrm{3}} \\ $$$$\sqrt{\mathrm{14}+\sqrt{\mathrm{3}}+\mathrm{2}−\sqrt{\mathrm{3}}}=\sqrt{\mathrm{16}}=\mathrm{4} \\ $$

Commented by liberty last updated on 17/Jan/21