The area of a square field is

The length of one side is equal to the square root of the area of the field. Hence, we just need to calculate the value of $\sqrt{30 \frac{1}{4}}$

We have;

$\sqrt{30 \frac{1}{4}}=\frac{\sqrt{121}}{\sqrt{4}}$

Now, calculating the square root of the numerator and the denominator:

$\sqrt{121}=\sqrt{11 \times 11}=11$

$\sqrt{4}=2$

Therefore, the length of the side of the square $=\sqrt{30 \frac{1}{4}}=\frac{11}{2}=5 \frac{1}{2} \mathrm{~m}$