12\sqrt{12}- 18\sqrt{18}+ 8\sqrt{8}- 3\sqrt{3}

asked by guest
on Jan 21, 2025 at 6:26 pm



You asked:

Evaluate the expression: 12−18+8−3\sqrt{12} - \sqrt{18} + \sqrt{8} - \sqrt{3}

MathBot Answer:

12−18+8−3=−2+3≈0.31783724519578224472575761729617\sqrt{12} - \sqrt{18} + \sqrt{8} - \sqrt{3} = - \sqrt{2} + \sqrt{3} \approx 0.31783724519578224472575761729617

12−18+8−3=2⋅3−18+8−3=2⋅3−3⋅2+8−3=2⋅3−3⋅2+2⋅2−3=(−3⋅2+2⋅3)+2⋅2−3=(−2+2⋅3)−3=3−2\begin{aligned}\sqrt{12} - \sqrt{18} + \sqrt{8} - \sqrt{3}&=2 \cdot \sqrt{3} - \sqrt{18} + \sqrt{8} - \sqrt{3}\\&=2 \cdot \sqrt{3} - 3 \cdot \sqrt{2} + \sqrt{8} - \sqrt{3}\\&=2 \cdot \sqrt{3} - 3 \cdot \sqrt{2} + 2 \cdot \sqrt{2} - \sqrt{3}\\&=\left(-3 \cdot \sqrt{2} + 2 \cdot \sqrt{3}\right) + 2 \cdot \sqrt{2} - \sqrt{3}\\&=\left(- \sqrt{2} + 2 \cdot \sqrt{3}\right) - \sqrt{3}\\&=\sqrt{3} - \sqrt{2}\end{aligned}

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