One fact to know

Let $N = \sqrt a \times \sqrt[3] a \times \sqrt a \times \sqrt[3] a \times \sqrt a = a^\frac 12 \times a^\frac 13 \times a^\frac 12 \times a^\frac 13 \times a^\frac 12 = a^{\frac {13}6}$ . For $N$ to be an integer, $a$ must has a power of 6, the smallest greater than 1 is $a=2^6 = \boxed{64}$ , then $N = 2^{13}=8192$ .

$\begin{aligned} &=\sqrt{a} \times \sqrt[3]{a} \times \sqrt{a} \times \sqrt[3]{a} \times \sqrt{a} \\ &= a^{\frac{1}{2}} \times a^{\frac{1}{3}} \times a^{\frac{1}{2}} \times a^{\frac{1}{3}} \times a^{\frac{1}{2}} \\ &= a^{\frac{15}{6}} \implies a = \text{Power of 6}\end{aligned}$

To minimise $a$ , it must have 6th power of 2 $\implies a = 2^6 = \boxed{64}$