Question

The value of ${\left[{\left(81\right)}^{\frac{1}{2}}\right]}^{\frac{1}{2}}$ is
(a) 3
(b) –3
(c) 9
(d) $\frac{1}{3}$

Answer 1

$$\begin{gathered} {\left[{\left(81\right)}^{\frac{1}{2}}\right]}^{\frac{1}{2}}={\left[{\left(3^4\right)}^{\frac{1}{2}}\right]}^{\frac{1}{2}} \\ ={\left[3^2\right]}^{\frac{1}{2}} \\ =3 \end{gathered}$$

$\therefore$The value of ${\left[{\left(81\right)}^{\frac{1}{2}}\right]}^{\frac{1}{2}}$ is 3.

Hence, the correct option is (a).