Rewrite the square root of the division $\sqrt{\frac{126}{23}}$ as the division of square roots $\frac{\sqrt{126}}{\sqrt{23}}$.
$$69\times \frac{\sqrt{126}}{\sqrt{23}}$$
Factor $126=3^{2}\times 14$. Rewrite the square root of the product $\sqrt{3^{2}\times 14}$ as the product of square roots $\sqrt{3^{2}}\sqrt{14}$. Take the square root of $3^{2}$.
$$69\times \frac{3\sqrt{14}}{\sqrt{23}}$$
Rationalize the denominator of $\frac{3\sqrt{14}}{\sqrt{23}}$ by multiplying numerator and denominator by $\sqrt{23}$.
