Question

The value of 27^1/3. 4^1/2 is

(a) 6

(b) 12

(c) 18

(d) − 6

Answer 1

Let us first simplify ${27}^{\frac{1}{2}}\mathrm{and}{4}^{\frac{1}{2}}$ separately.
$$\begin{gathered} {27}^{\frac{1}{3}}={\left(3^3\right)}^{\frac{1}{3}}=3^{3\times \frac{1}{3}}=3^1=3 \\ {4}^{\frac{1}{2}}={\left(2^2\right)}^{\frac{1}{2}}=2^{2\times \frac{1}{2}}=2^1=2 \end{gathered}$$
Therefore
${27}^{\frac{1}{3}}·4^{\frac{1}{2}}=3\times 2=6$
Hence, the correct option is (a).