Question Number 68740 by ahmadshah last updated on 15/Sep/19
![](https://www.tinkutara.com/question/9301.png)
Commented by Prithwish sen last updated on 15/Sep/19
![(√(30(√(30(√(30(√(30))(√(30(30^2 )^(1/2) )))))))) =(√(30(√(30(√(30(√(30))(√((30)^2 )))))))) =(√(30(√(30(√((30)^(5/2) )))))) =(√(30(√(30.(30)^(5/4) )))) =(√(30(√((30)^(9/4) )))) =(√(30.(30)^(9/8) )) =(30^((17)/8) )^(1/2) = 30^((17)/(16))](https://www.tinkutara.com/question/Q68753.png)
$$\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}}\sqrt{\mathrm{30}\left(\mathrm{30}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} }}}} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}}\sqrt{\left(\mathrm{30}\right)^{\mathrm{2}} }}}} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\left(\mathrm{30}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} }}} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\mathrm{30}.\left(\mathrm{30}\right)^{\frac{\mathrm{5}}{\mathrm{4}}} }} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\left(\mathrm{30}\right)^{\frac{\mathrm{9}}{\mathrm{4}}} }} \\ $$$$=\sqrt{\mathrm{30}.\left(\mathrm{30}\right)^{\frac{\mathrm{9}}{\mathrm{8}}} } \\ $$$$=\left(\mathrm{30}^{\frac{\mathrm{17}}{\mathrm{8}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =\:\mathrm{30}^{\frac{\mathrm{17}}{\mathrm{16}}} \\ $$
Answered by MJS last updated on 15/Sep/19
![30^((17)/(16))](https://www.tinkutara.com/question/Q68742.png)
$$\mathrm{30}^{\frac{\mathrm{17}}{\mathrm{16}}} \\ $$