43+52−23+72−24\sqrt[]{3}+5\sqrt[]{2}-2\sqrt[]{3}+7\sqrt[]{2}-\sqrt[]{2}

asked by guest
on Mar 16, 2025 at 10:24 pm



You asked:

Evaluate the expression: 43+52−23+72−24 \sqrt{3} + 5 \sqrt{2} - 2 \sqrt{3} + 7 \sqrt{2} - \sqrt{2}

MathBot Answer:

43+52−23+72−2=23+112≈19.020450801241800123873468649318424 \sqrt{3} + 5 \sqrt{2} - 2 \sqrt{3} + 7 \sqrt{2} - \sqrt{2} = 2 \sqrt{3} + 11 \sqrt{2} \approx 19.02045080124180012387346864931842

43+52−23+72−2=4⋅3+5⋅2−2⋅3+7⋅2−2=(4⋅3+5⋅2)−2⋅3+7⋅2−2=(2⋅3+5⋅2)+7⋅2−2=(2⋅3+12⋅2)−2=2⋅3+11⋅2\begin{aligned}4 \sqrt{3} + 5 \sqrt{2} - 2 \sqrt{3} + 7 \sqrt{2} - \sqrt{2}&=4 \cdot \sqrt{3} + 5 \cdot \sqrt{2} - 2 \cdot \sqrt{3} + 7 \cdot \sqrt{2} - \sqrt{2}\\&=\left(4 \cdot \sqrt{3} + 5 \cdot \sqrt{2}\right) - 2 \cdot \sqrt{3} + 7 \cdot \sqrt{2} - \sqrt{2}\\&=\left(2 \cdot \sqrt{3} + 5 \cdot \sqrt{2}\right) + 7 \cdot \sqrt{2} - \sqrt{2}\\&=\left(2 \cdot \sqrt{3} + 12 \cdot \sqrt{2}\right) - \sqrt{2}\\&=2 \cdot \sqrt{3} + 11 \cdot \sqrt{2}\end{aligned}

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