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

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



You asked:

Evaluate the expression: \(3 \cdot \sqrt{20} + 2 \cdot \sqrt{45} + \sqrt{80}\)

MathBot Answer:

\[3 \cdot \sqrt{20} + 2 \cdot \sqrt{45} + \sqrt{80} = 16 \sqrt{5} \approx 35.77708763999663514254677869970042\]

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

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