The value of

$7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}$

$=(7 \times 8)^{\frac{1}{2}} \quad\left[x^{a} \times y^{a}=(x \times y)^{a}\right]$

$=(56)^{\frac{1}{2}}$

Hence, the correct answer is option (b).