Question:
The value of $7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}$ is
(a) $(28)^{1 / 2}$
(b) $(56)^{1 / 2}$
(c) $(14)^{1 / 2}$
(d) $(42)^{1 / 2}$
Solution:
$7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}$
$=(7 \times 8)^{\frac{1}{2}} \quad\left[x^{a} \times y^{a}=(x \times y)^{a}\right]$
$=(56)^{\frac{1}{2}}$
Hence, the correct answer is option (b).