1.35/3*(31.56+22.08+√31.56*22.08)

asked by guest
on Nov 25, 2024 at 9:42 pm



You asked:

Evaluate the expression: \(\frac{1.35}{3} \cdot \left(31.56 + 22.08 + \sqrt{31.56} \cdot 22.08\right)\)

MathBot Answer:

\[\frac{1.35}{3} \cdot \left(31.56 + 22.08 + \sqrt{31.56} \cdot 22.08\right) = \frac{12069}{500} + \frac{1242 \sqrt{789}}{625} \approx 79.95674657997974070954138208777699\]

\[\begin{aligned}\frac{1.35}{3} \cdot \left(31.56 + 22.08 + \sqrt{31.56} \cdot 22.08\right)& = \left(1 + \frac{35}{100}\right) \cdot \frac{1}{3} \cdot \left(31 + \frac{56}{100} + 22 + \frac{8}{100} + \sqrt{31 + \frac{56}{100}} \cdot \left(22 + \frac{8}{100}\right)\right)\\& = \left(1 + \frac{7}{20}\right) \cdot \frac{1}{3} \cdot \left(31 + \frac{56}{100} + 22 + \frac{8}{100} + \sqrt{31 + \frac{56}{100}} \cdot \left(22 + \frac{8}{100}\right)\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{56}{100} + 22 + \frac{8}{100} + \sqrt{31 + \frac{56}{100}} \cdot \left(22 + \frac{8}{100}\right)\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{14}{25} + 22 + \frac{8}{100} + \sqrt{31 + \frac{56}{100}} \cdot \left(22 + \frac{8}{100}\right)\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{14}{25} + 22 + \frac{2}{25} + \sqrt{31 + \frac{56}{100}} \cdot \left(22 + \frac{8}{100}\right)\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{14}{25} + 22 + \frac{2}{25} + \sqrt{31 + \frac{14}{25}} \cdot \left(22 + \frac{8}{100}\right)\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{14}{25} + 22 + \frac{2}{25} + \sqrt{\frac{789}{25}} \cdot \left(22 + \frac{8}{100}\right)\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{14}{25} + 22 + \frac{2}{25} + \frac{1}{5} \cdot \sqrt{789} \cdot \left(22 + \frac{8}{100}\right)\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{14}{25} + 22 + \frac{2}{25} + \frac{1}{5} \cdot \sqrt{789} \cdot \left(22 + \frac{2}{25}\right)\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{14}{25} + 22 + \frac{2}{25} + \frac{1}{5} \cdot \sqrt{789} \cdot \frac{552}{25}\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(31 + \frac{14}{25} + 22 + \frac{2}{25} + \frac{552}{125} \cdot \sqrt{789}\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(\frac{789}{25} + 22 + \frac{2}{25} + \frac{552}{125} \cdot \sqrt{789}\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(\frac{1339}{25} + \frac{2}{25} + \frac{552}{125} \cdot \sqrt{789}\right)\\& = \frac{27}{20} \cdot \frac{1}{3} \cdot \left(\frac{1341}{25} + \frac{552}{125} \cdot \sqrt{789}\right)\\& = \frac{9}{20} \cdot \left(\frac{1341}{25} + \frac{552}{125} \cdot \sqrt{789}\right)\\& = \frac{12069}{500} + \frac{1242}{625} \cdot \sqrt{789}\end{aligned}\]

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