26. \( \sqrt{15 \cdot 3-\frac{126}{14}} \) 27. \( \frac{16}{9}+\frac{1}{6} \cdot \frac{9}{4} \)

Calculate or simplify the expression \( \sqrt{15 \cdot 3-\frac{126}{14}} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{15\times 3-\frac{126}{14}}\) - step1: Divide the terms: \(\sqrt{15\times 3-9}\) - step2: Multiply the numbers: \(\sqrt{45-9}\) - step3: Subtract the numbers: \(\sqrt{36}\) - step4: Write in exponential form: \(\sqrt{6^{2}}\) - step5: Simplify the root: \(6\) Calculate or simplify the expression \( \frac{16}{9}+\frac{1}{6} \cdot \frac{9}{4} \). Calculate the value by following steps: - step0: Calculate: \(\frac{16}{9}+\frac{1}{6}\times \frac{9}{4}\) - step1: Multiply the numbers: \(\frac{16}{9}+\frac{3}{8}\) - step2: Reduce fractions to a common denominator: \(\frac{16\times 8}{9\times 8}+\frac{3\times 9}{8\times 9}\) - step3: Multiply the numbers: \(\frac{16\times 8}{72}+\frac{3\times 9}{8\times 9}\) - step4: Multiply the numbers: \(\frac{16\times 8}{72}+\frac{3\times 9}{72}\) - step5: Transform the expression: \(\frac{16\times 8+3\times 9}{72}\) - step6: Multiply the numbers: \(\frac{128+3\times 9}{72}\) - step7: Multiply the numbers: \(\frac{128+27}{72}\) - step8: Add the numbers: \(\frac{155}{72}\) The solutions to the given expressions are: 1. \( \sqrt{15 \cdot 3-\frac{126}{14}} = 6 \) 2. \( \frac{16}{9}+\frac{1}{6} \cdot \frac{9}{4} = \frac{155}{72} \) or \( 2\frac{11}{72} \) or \( 2.152\dot{7} \)