2√50-3√18+2√2

asked by guest
on Apr 01, 2025 at 10:12 am



You asked:

Evaluate the expression: 250−318+222 \sqrt{50} - 3 \sqrt{18} + 2 \sqrt{2}

MathBot Answer:

250−318+22=32≈4.242640687119285146405066172629092 \sqrt{50} - 3 \sqrt{18} + 2 \sqrt{2} = 3 \sqrt{2} \approx 4.24264068711928514640506617262909

250−318+22=2⋅50−3⋅18+2⋅2=2⋅5⋅2−3⋅18+2⋅2=10⋅2−3⋅18+2⋅2=10⋅2−3⋅3⋅2+2⋅2=10⋅2−9⋅2+2⋅2=2+2⋅2=3⋅2\begin{aligned}2 \sqrt{50} - 3 \sqrt{18} + 2 \sqrt{2}&=2 \cdot \sqrt{50} - 3 \cdot \sqrt{18} + 2 \cdot \sqrt{2}\\&=2 \cdot 5 \cdot \sqrt{2} - 3 \cdot \sqrt{18} + 2 \cdot \sqrt{2}\\&=10 \cdot \sqrt{2} - 3 \cdot \sqrt{18} + 2 \cdot \sqrt{2}\\&=10 \cdot \sqrt{2} - 3 \cdot 3 \cdot \sqrt{2} + 2 \cdot \sqrt{2}\\&=10 \cdot \sqrt{2} - 9 \cdot \sqrt{2} + 2 \cdot \sqrt{2}\\&=\sqrt{2} + 2 \cdot \sqrt{2}\\&=3 \cdot \sqrt{2}\end{aligned}

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