43+5223+7224\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+5223+7224 \sqrt{3} + 5 \sqrt{2} - 2 \sqrt{3} + 7 \sqrt{2} - \sqrt{2}

MathBot Answer:

43+5223+722=23+11219.020450801241800123873468649318424 \sqrt{3} + 5 \sqrt{2} - 2 \sqrt{3} + 7 \sqrt{2} - \sqrt{2} = 2 \sqrt{3} + 11 \sqrt{2} \approx 19.02045080124180012387346864931842


43+5223+722=43+5223+722=(43+52)23+722=(23+52)+722=(23+122)2=23+112\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}