How can I solve this problem $\sqrt{30 \sqrt{30 \sqrt{30 ...}}}$

$\begingroup$

How can I solve this problem $\underbrace{\sqrt{30 \sqrt{30 \sqrt{30 ...}}}}_{10 \text{ times}}$

Should I calculate it straight forward way adding the indices

$\endgroup$

1 Answer

$\begingroup$

HINT:

$$=30^{1/2+1/4+\cdots+\text{ up to ten terms}}$$

Observe that the exponent is in Geometric Series

$\endgroup$ 1