Convert the mixed number 4 (29)/(49) into an improper fraction.

To do this, multiply the whole number by the denominator and add the numerator. Keep the same denominator.

$$4 \frac{29}{49} = \frac{(4 \times 49) + 29}{49}$$ $$= \frac{196 + 29}{49}$$ $$= \frac{225}{49}$$

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

$$\sqrt{\frac{225}{49}} = \frac{\sqrt{225}}{\sqrt{49}}$$

$$\sqrt{225} = 15$$ $$\sqrt{49} = 7$$

$$\frac{15}{7}$$

This can also be expressed as a mixed number:

$$\frac{15}{7} = 2 \frac{1}{7}$$

The square root of $4 \frac{29}{49}$ is $\boxed*{\frac{15}{7}}$ or $\boxed*{2 \frac{1}{7}}$.