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: 1.353(31.56+22.08+31.5622.08)\frac{1.35}{3} \left(31.56 + 22.08 + \sqrt{31.56} \cdot 22.08\right)

MathBot Answer:

1.353(31.56+22.08+31.5622.08)=12069500+124278962579.95674657997974070954138208777699\frac{1.35}{3} \left(31.56 + 22.08 + \sqrt{31.56} \cdot 22.08\right) = \frac{12069}{500} + \frac{1242 \sqrt{789}}{625} \approx 79.95674657997974070954138208777699


1.353(31.56+22.08+31.5622.08)=(1+35100)13(31+56100+22+8100+31+56100(22+8100))=(1+720)13(31+56100+22+8100+31+56100(22+8100))=272013(31+56100+22+8100+31+56100(22+8100))=272013(31+1425+22+8100+31+56100(22+8100))=272013(31+1425+22+225+31+56100(22+8100))=272013(31+1425+22+225+31+1425(22+8100))=272013(31+1425+22+225+78925(22+8100))=272013(31+1425+22+225+15789(22+8100))=272013(31+1425+22+225+15789(22+225))=272013(31+1425+22+225+1578955225)=272013(31+1425+22+225+552125789)=272013(78925+22+225+552125789)=272013(133925+225+552125789)=272013(134125+552125789)=920(134125+552125789)=12069500+1242625789\begin{aligned}\frac{1.35}{3} \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}