1156 b

$\sqrt{\frac{a}{b}\sqrt{\frac{b}{a}\sqrt{\frac{a}{b}}}}=\sqrt{\frac{a}{b}\sqrt{\frac{b}{a}*\frac{a^{0,5}}{b^{0,5}}}}=\sqrt{\frac{a}{b}\sqrt{\frac{b^{0,5}}{a^{0,5}}}}=\sqrt{\frac{a}{b}*\frac{b^{0,25}}{a^{0,25}}}=\sqrt{\frac{a^{0,75}}{b^{0,75}}}=\frac{a^{0,75/2}}{b^{0,75/2}}$

0,75/2 = (3/4)/2 = 3/8.