15-3√1/81

To simplify the expression \( 15 - 3\sqrt{\frac{1}{81}} \), we can start by simplifying \( \sqrt{\frac{1}{81}} \). Since \( 81 = 9^2 \), we have: \[ \sqrt{81} = 9 \] Thus: \[ \sqrt{\frac{1}{81}} = \frac{1}{\sqrt{81}} = \frac{1}{9} \] Now, substituting this back into the original expression: \[ 15 - 3\sqrt{\frac{1}{81}} = 15 - 3 \left(\frac{1}{9}\right) \] Next, we calculate \( 3 \left(\frac{1}{9}\right) \): \[ 3 \times \frac{1}{9} = \frac{3}{9} = \frac{1}{3} \] Now substitute that back into the expression: \[ 15 - \frac{1}{3} \] To combine these, we can convert 15 to a fraction with a denominator of 3: \[ 15 = \frac{45}{3} \] Now we can subtract: \[ \frac{45}{3} - \frac{1}{3} = \frac{45 - 1}{3} = \frac{44}{3} \] So, the simplified result is: \[ \frac{44}{3} \]