3 20\sqrt{20} +2 $\sqrt{\45}$ + 80\sqrt{80}

asked by guest
on Nov 26, 2024 at 12:26 pm



You asked:

Evaluate the expression: 320+245+803 \sqrt{20} + 2 \sqrt{45} + \sqrt{80}

MathBot Answer:

320+245+80=165≈35.777087639996635142546778699700423 \sqrt{20} + 2 \sqrt{45} + \sqrt{80} = 16 \sqrt{5} \approx 35.77708763999663514254677869970042

320+245+80=3⋅20+2⋅45+80=3⋅2⋅5+2⋅45+80=6⋅5+2⋅45+80=6⋅5+2⋅3⋅5+80=6⋅5+6⋅5+80=6⋅5+6⋅5+4⋅5=12⋅5+4⋅5=16⋅5\begin{aligned}3 \sqrt{20} + 2 \sqrt{45} + \sqrt{80}&=3 \cdot \sqrt{20} + 2 \cdot \sqrt{45} + \sqrt{80}\\&=3 \cdot 2 \cdot \sqrt{5} + 2 \cdot \sqrt{45} + \sqrt{80}\\&=6 \cdot \sqrt{5} + 2 \cdot \sqrt{45} + \sqrt{80}\\&=6 \cdot \sqrt{5} + 2 \cdot 3 \cdot \sqrt{5} + \sqrt{80}\\&=6 \cdot \sqrt{5} + 6 \cdot \sqrt{5} + \sqrt{80}\\&=6 \cdot \sqrt{5} + 6 \cdot \sqrt{5} + 4 \cdot \sqrt{5}\\&=12 \cdot \sqrt{5} + 4 \cdot \sqrt{5}\\&=16 \cdot \sqrt{5}\end{aligned}

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