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:

\[ \frac{44}{3} \]