2 50\sqrt{50} -8 18\sqrt{18} +3 72\sqrt{72}

asked by guest
on Nov 17, 2024 at 1:22 pm



You asked:

Evaluate the expression: 250−818+3722 \sqrt{50} - 8 \sqrt{18} + 3 \sqrt{72}

MathBot Answer:

250−818+372=42≈5.656854249492380195206754896838792 \sqrt{50} - 8 \sqrt{18} + 3 \sqrt{72} = 4 \sqrt{2} \approx 5.65685424949238019520675489683879

250−818+372=2⋅50−8⋅18+3⋅72=2⋅5⋅2−8⋅18+3⋅72=10⋅2−8⋅18+3⋅72=10⋅2−8⋅3⋅2+3⋅72=10⋅2−24⋅2+3⋅72=10⋅2−24⋅2+3⋅6⋅2=10⋅2−24⋅2+18⋅2=−14⋅2+18⋅2=4⋅2\begin{aligned}2 \sqrt{50} - 8 \sqrt{18} + 3 \sqrt{72}&=2 \cdot \sqrt{50} - 8 \cdot \sqrt{18} + 3 \cdot \sqrt{72}\\&=2 \cdot 5 \cdot \sqrt{2} - 8 \cdot \sqrt{18} + 3 \cdot \sqrt{72}\\&=10 \cdot \sqrt{2} - 8 \cdot \sqrt{18} + 3 \cdot \sqrt{72}\\&=10 \cdot \sqrt{2} - 8 \cdot 3 \cdot \sqrt{2} + 3 \cdot \sqrt{72}\\&=10 \cdot \sqrt{2} - 24 \cdot \sqrt{2} + 3 \cdot \sqrt{72}\\&=10 \cdot \sqrt{2} - 24 \cdot \sqrt{2} + 3 \cdot 6 \cdot \sqrt{2}\\&=10 \cdot \sqrt{2} - 24 \cdot \sqrt{2} + 18 \cdot \sqrt{2}\\&=-14 \cdot \sqrt{2} + 18 \cdot \sqrt{2}\\&=4 \cdot \sqrt{2}\end{aligned}

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