Question Number 190512 by 073 last updated on 04/Apr/23
Answered by som(math1967) last updated on 04/Apr/23
$$\:^{\mathrm{3}} \sqrt{\sqrt{\mathrm{15}}+\frac{\mathrm{196}}{\mathrm{54}}} \\ $$$$=\:^{\mathrm{3}} \sqrt{\sqrt{\mathrm{15}}+\frac{\mathrm{98}}{\mathrm{27}}} \\ $$$$=^{\mathrm{3}} \sqrt{\frac{\mathrm{27}\sqrt{\mathrm{15}}+\mathrm{98}}{\mathrm{27}}} \\ $$$$=\:^{\mathrm{3}} \sqrt{\frac{\mathrm{8}+\mathrm{3}.\mathrm{2}.\mathrm{15}+\mathrm{3}.\mathrm{4}.\sqrt{\mathrm{15}}+\mathrm{15}\sqrt{\mathrm{15}}}{\mathrm{3}^{\mathrm{3}} }} \\ $$$$=\:^{\mathrm{3}} \sqrt{\frac{\left(\mathrm{2}+\sqrt{\mathrm{15}}\right)^{\mathrm{3}} }{\mathrm{3}^{\mathrm{3}} }} \\ $$$$=\frac{{a}}{\mathrm{3}} \\ $$