15-3√1/81

To simplify the expression \( 15 - 3\sqrt{\frac{1}{81}} \), we can start by simplifying the square root term. 1. First, simplify \( \sqrt{\frac{1}{81}} \): \[ \sqrt{\frac{1}{81}} = \frac{\sqrt{1}}{\sqrt{81}} = \frac{1}{9} \] 2. Now substitute \( \frac{1}{9} \) back into the expression: \[ 15 - 3\left(\frac{1}{9}\right) \] 3. Multiply \( 3 \) by \( \frac{1}{9} \): \[ 3 \times \frac{1}{9} = \frac{3}{9} = \frac{1}{3} \] 4. Now replace that in the original expression: \[ 15 - \frac{1}{3} \] 5. To subtract \( \frac{1}{3} \) from \( 15 \), convert \( 15 \) to have a common denominator of 3: \[ 15 = \frac{45}{3} \] 6. Now perform the subtraction: \[ \frac{45}{3} - \frac{1}{3} = \frac{45 - 1}{3} = \frac{44}{3} \] So, the simplified result of the expression \( 15 - 3\sqrt{\frac{1}{81}} \) is: \[ \frac{44}{3} \]