($\sqrt{25/9}$ + $\sqrt{64/25}$ - $\sqrt{121/225}$)*( $\sqrt{49/36}$ - $\sqrt{25/36}$ )

asked by guest
on Sep 19, 2024 at 6:06 pm



You asked:

Evaluate the expression: \(\left(\sqrt{\frac{25}{9}} + \sqrt{\frac{64}{25}} - \sqrt{\frac{121}{225}}\right) \cdot \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)\)

MathBot Answer:

\[\left(\sqrt{\frac{25}{9}} + \sqrt{\frac{64}{25}} - \sqrt{\frac{121}{225}}\right) \cdot \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right) = \frac{38}{45} = 0.8\overline{4}\]

\[\begin{aligned}\left(\sqrt{\frac{25}{9}} + \sqrt{\frac{64}{25}} - \sqrt{\frac{121}{225}}\right) \cdot \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)& = \left(\frac{5}{3} + \sqrt{\frac{64}{25}} - \sqrt{\frac{121}{225}}\right) \cdot \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)\\& = \left(\frac{5}{3} + \frac{8}{5} - \sqrt{\frac{121}{225}}\right) \cdot \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)\\& = \left(\frac{5}{3} + \frac{8}{5} - \frac{11}{15}\right) \cdot \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)\\& = \left(\frac{49}{15} - \frac{11}{15}\right) \cdot \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)\\& = \frac{38}{15} \cdot \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)\\& = \frac{38}{15} \cdot \left(\frac{7}{6} - \sqrt{\frac{25}{36}}\right)\\& = \frac{38}{15} \cdot \left(\frac{7}{6} - \frac{5}{6}\right)\\& = \frac{38}{15} \cdot \frac{1}{3}\\& = \frac{38}{45}\end{aligned}\]

+ Submit Question