√1.21•0.09.0.0001

To solve the expression \(\sqrt{1.21 \cdot 0.09 \cdot 0.0001}\), we can break it down step by step. 1. **Calculate the product inside the square root:** - First, multiply the three numbers together: \[ 1.21 \cdot 0.09 = 0.1089 \] Now, we multiply this result by \(0.0001\): \[ 0.1089 \cdot 0.0001 = 0.00001089 \] 2. **Now, take the square root of the product:** \[ \sqrt{0.00001089} \] To simplify: - \(0.00001089\) can be rewritten as \(10^{-5} \cdot 10.89\), which leads to: \[ = \sqrt{10^{-5} \cdot 10.89} = \sqrt{10^{-5}} \cdot \sqrt{10.89} \] - \(\sqrt{10^{-5}} = 10^{-2.5} = 0.01\) - \(\sqrt{10.89} = 3.3\) (since \(10.89 = 3.3^2\)) 3. **Combine the results:** \[ 0.01 \cdot 3.3 = 0.033 \] Therefore, \(\sqrt{1.21 \cdot 0.09 \cdot 0.0001} = 0.033\).