2) \( \left(1+\frac{1}{2}\right)^{2}-\sqrt{2+\frac{1}{11}}-\frac{3}{5}= \)

Calculate or simplify the expression \( (1+1/2)^2-\sqrt(2+1/11)-3/5 \). Calculate the value by following steps: - step0: Calculate: \(\left(1+\frac{1}{2}\right)^{2}-\sqrt{2+\frac{1}{11}}-\frac{3}{5}\) - step1: Add the numbers: \(\left(\frac{3}{2}\right)^{2}-\sqrt{2+\frac{1}{11}}-\frac{3}{5}\) - step2: Add the numbers: \(\left(\frac{3}{2}\right)^{2}-\sqrt{\frac{23}{11}}-\frac{3}{5}\) - step3: Simplify the root: \(\left(\frac{3}{2}\right)^{2}-\frac{\sqrt{253}}{11}-\frac{3}{5}\) - step4: Evaluate the power: \(\frac{9}{4}-\frac{\sqrt{253}}{11}-\frac{3}{5}\) - step5: Reduce fractions to a common denominator: \(\frac{9\times 11\times 5}{4\times 11\times 5}-\frac{\sqrt{253}\times 4\times 5}{11\times 4\times 5}-\frac{3\times 4\times 11}{5\times 4\times 11}\) - step6: Multiply the terms: \(\frac{9\times 11\times 5}{220}-\frac{\sqrt{253}\times 4\times 5}{11\times 4\times 5}-\frac{3\times 4\times 11}{5\times 4\times 11}\) - step7: Multiply the terms: \(\frac{9\times 11\times 5}{220}-\frac{\sqrt{253}\times 4\times 5}{220}-\frac{3\times 4\times 11}{5\times 4\times 11}\) - step8: Multiply the terms: \(\frac{9\times 11\times 5}{220}-\frac{\sqrt{253}\times 4\times 5}{220}-\frac{3\times 4\times 11}{220}\) - step9: Transform the expression: \(\frac{9\times 11\times 5-\sqrt{253}\times 4\times 5-3\times 4\times 11}{220}\) - step10: Multiply the terms: \(\frac{495-\sqrt{253}\times 4\times 5-3\times 4\times 11}{220}\) - step11: Multiply the terms: \(\frac{495-20\sqrt{253}-3\times 4\times 11}{220}\) - step12: Multiply the terms: \(\frac{495-20\sqrt{253}-132}{220}\) - step13: Subtract the numbers: \(\frac{363-20\sqrt{253}}{220}\) La expresión \( \left(1+\frac{1}{2}\right)^{2}-\sqrt{2+\frac{1}{11}}-\frac{3}{5} \) es aproximadamente igual a 0.204002.