0. \( \sqrt{\frac{81}{225}} \) 3. \( \sqrt{\frac{36}{121}} \) 6. \( \sqrt{-\frac{100}{0,01}} \) 29. \( \sqrt{2 \frac{47}{121}} \)

Let's simplify each of the expressions step by step. 0. \( \sqrt{\frac{81}{225}} \) First, we can simplify the fraction inside the square root: \[ \frac{81}{225} = \frac{9^2}{15^2} = \left(\frac{9}{15}\right)^2 = \left(\frac{3}{5}\right)^2 \] Now, taking the square root: \[ \sqrt{\frac{81}{225}} = \frac{3}{5} \] --- 3. \( \sqrt{\frac{36}{121}} \) Similarly, we simplify the fraction: \[ \frac{36}{121} = \frac{6^2}{11^2} = \left(\frac{6}{11}\right)^2 \] Now, taking the square root: \[ \sqrt{\frac{36}{121}} = \frac{6}{11} \] --- 6. \( \sqrt{-\frac{100}{0.01}} \) First, simplify the fraction: \[ \frac{100}{0.01} = \frac{100}{\frac{1}{100}} = 100 \times 100 = 10000 \] Now, we have: \[ \sqrt{-10000} \] Since we are taking the square root of a negative number, we can express this in terms of imaginary numbers: \[ \sqrt{-10000} = \sqrt{10000} \cdot i = 100 \cdot i = 100i \] --- 29. \( \sqrt{2 \frac{47}{121}} \) First, convert the mixed number into an improper fraction: \[ 2 \frac{47}{121} = \frac{2 \cdot 121 + 47}{121} = \frac{242 + 47}{121} = \frac{289}{121} \] Now, we take the square root: \[ \sqrt{2 \frac{47}{121}} = \sqrt{\frac{289}{121}} = \frac{\sqrt{289}}{\sqrt{121}} = \frac{17}{11} \] --- In summary, the simplified results are: 0. \( \frac{3}{5} \) 3. \( \frac{6}{11} \) 6. \( 100i \) 29. \( \frac{17}{11} \)