Convert the mixed number 23 (26)/(121) into an improper fraction.

Multiply the whole number by the denominator and add the numerator. Keep the same denominator.

$$23 \frac{26}{121} = \frac{(23 \times 121) + 26}{121}$$ $$= \frac{2783 + 26}{121}$$ $$= \frac{2809}{121}$$

To find the square root of a fraction, take the square root of the numerator and the square root of the denominator separately.

$$\sqrt{\frac{2809}{121}} = \frac{\sqrt{2809}}{\sqrt{121}}$$

$$\sqrt{2809} = 53$$ $$\sqrt{121} = 11$$

$$\frac{53}{11}$$

This can also be expressed as a mixed number:

$$\frac{53}{11} = 4 \frac{9}{11}$$

The square root of $23 \frac{26}{121}$ is $\boxed*{\frac{53}{11}}$ or $\boxed*{4 \frac{9}{11}}$.