Question

If $\sqrt{3^n}=81$, then $n=?$

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (D)

$8$

Given, $\sqrt{3^n}=81$

Since, $\sqrt{\left(3^n\right)}=3^{n/2}$ and $81=3^4$

So, $3^{n/2}=3^4$,

$\Rightarrow \frac{n}{2}=4$ (As bases are equal, their powers has to be) equal.

$\Rightarrow n=8$