b) 3sqrt ((25)/(9))+15sqrt ((16)/(25))=

To solve the expression \(3\sqrt{\frac{25}{9}} + 15\sqrt{\frac{16}{25}}\), we need to simplify each square root term separately.<br /><br />First, let's simplify \(\sqrt{\frac{25}{9}}\):<br />\[<br />\sqrt{\frac{25}{9}} = \frac{\sqrt{25}}{\sqrt{9}} = \frac{5}{3}<br />\]<br /><br />Next, let's simplify \(\sqrt{\frac{16}{25}}\):<br />\[<br />\sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}<br />\]<br /><br />Now, substitute these simplified values back into the original expression:<br />\[<br />3\sqrt{\frac{25}{9}} + 15\sqrt{\frac{16}{25}} = 3 \cdot \frac{5}{3} + 15 \cdot \frac{4}{5}<br />\]<br /><br />Simplify each term:<br />\[<br />3 \cdot \frac{5}{3} = 5<br />\]<br />\[<br />15 \cdot \frac{4}{5} = 15 \cdot \frac{4}{5} = 3 \cdot 4 = 12<br />\]<br /><br />Finally, add the two results together:<br />\[<br />5 + 12 = 17<br />\]<br /><br />Thus, the value of the expression is:<br />\[<br />\boxed{17}<br />\]