Question

The value of $7^{\frac{1}{2}}·8^{\frac{1}{2}}$ is
(a) (28)^1/2
(b) (56)^1/2
(c) (14)^1/2
(d) (42)^1/2

Answer 1

$$\begin{gathered} 7^{\frac{1}{2}}·8^{\frac{1}{2}} \\ ={\left(7\times 8\right)}^{\frac{1}{2}}\left[x^a\times y^a={\left(x\times y\right)}^a\right] \\ ={\left(56\right)}^{\frac{1}{2}} \end{gathered}$$
Hence, the correct answer is option (b).