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

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



You asked:

Evaluate the expression: (259+6425−121225)(4936−2536)\left(\sqrt{\frac{25}{9}} + \sqrt{\frac{64}{25}} - \sqrt{\frac{121}{225}}\right) \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)

MathBot Answer:

(259+6425−121225)(4936−2536)=3845=0.84‾\left(\sqrt{\frac{25}{9}} + \sqrt{\frac{64}{25}} - \sqrt{\frac{121}{225}}\right) \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right) = \frac{38}{45} = 0.8\overline{4}

(259+6425−121225)(4936−2536)=(259+6425−121225)⋅(4936−2536)=(53+6425−121225)⋅(4936−2536)=(53+85−121225)⋅(4936−2536)=(53+85−1115)⋅(4936−2536)=(4915−1115)⋅(4936−2536)=3815⋅(4936−2536)=3815⋅(76−2536)=3815⋅(76−56)=3815⋅13=3845\begin{aligned}\left(\sqrt{\frac{25}{9}} + \sqrt{\frac{64}{25}} - \sqrt{\frac{121}{225}}\right) \left(\sqrt{\frac{49}{36}} - \sqrt{\frac{25}{36}}\right)&=\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}

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