Express $89\times \frac{59}{6}$ as a single fraction.
$$\frac{89\times 59}{6}\sqrt{568}$$
Multiply $89$ and $59$ to get $5251$.
$$\frac{5251}{6}\sqrt{568}$$
Factor $568=2^{2}\times 142$. Rewrite the square root of the product $\sqrt{2^{2}\times 142}$ as the product of square roots $\sqrt{2^{2}}\sqrt{142}$. Take the square root of $2^{2}$.
$$\frac{5251}{6}\times 2\sqrt{142}$$
Express $\frac{5251}{6}\times 2$ as a single fraction.
$$\frac{5251\times 2}{6}\sqrt{142}$$
Multiply $5251$ and $2$ to get $10502$.
$$\frac{10502}{6}\sqrt{142}$$
Reduce the fraction $\frac{10502}{6}$ to lowest terms by extracting and canceling out $2$.
