(-√3 - √2)² -4 -2√6/3 + √6³

asked by guest
on Nov 17, 2024 at 6:20 pm



You asked:

Evaluate the expression: (−3−2)2−4−263+63{\left( -\sqrt{3} - \sqrt{2} \right)}^{2} - 4 - \frac{2 \sqrt{6}}{3} + {\sqrt{6}}^{3}

MathBot Answer:

(−3−2)2−4−263+63=−4+(−3−2)2+1663≈18.9629247804099727201134165478432{\left( -\sqrt{3} - \sqrt{2} \right)}^{2} - 4 - \frac{2 \sqrt{6}}{3} + {\sqrt{6}}^{3} = -4 + \left(- \sqrt{3} - \sqrt{2}\right)^{2} + \frac{16 \sqrt{6}}{3} \approx 18.9629247804099727201134165478432

(−3−2)2−4−263+63=(−3−2)2−4−2⋅6⋅13+(6)3=(−2−3)2−4−2⋅6⋅13+(6)3=(−2−3)2−4−2⋅13⋅6+(6)3=(−2−3)2−4−23⋅6+(6)3=(−2−3)2−4−23⋅6+6⋅6=(−4+(−2−3)2)−23⋅6+6⋅6=(−4+(−2−3)2−23⋅6)+6⋅6=−4+(−2−3)2+163⋅6\begin{aligned}{\left( -\sqrt{3} - \sqrt{2} \right)}^{2} - 4 - \frac{2 \sqrt{6}}{3} + {\sqrt{6}}^{3}&=\left(- \sqrt{3} - \sqrt{2}\right)^{2} - 4 - 2 \cdot \sqrt{6} \cdot \frac{1}{3} + \left(\sqrt{6}\right)^{3}\\&=\left(- \sqrt{2} - \sqrt{3}\right)^{2} - 4 - 2 \cdot \sqrt{6} \cdot \frac{1}{3} + \left(\sqrt{6}\right)^{3}\\&=\left(- \sqrt{2} - \sqrt{3}\right)^{2} - 4 - 2 \cdot \frac{1}{3} \cdot \sqrt{6} + \left(\sqrt{6}\right)^{3}\\&=\left(- \sqrt{2} - \sqrt{3}\right)^{2} - 4 - \frac{2}{3} \cdot \sqrt{6} + \left(\sqrt{6}\right)^{3}\\&=\left(- \sqrt{2} - \sqrt{3}\right)^{2} - 4 - \frac{2}{3} \cdot \sqrt{6} + 6 \cdot \sqrt{6}\\&=\left(-4 + \left(- \sqrt{2} - \sqrt{3}\right)^{2}\right) - \frac{2}{3} \cdot \sqrt{6} + 6 \cdot \sqrt{6}\\&=\left(-4 + \left(- \sqrt{2} - \sqrt{3}\right)^{2} - \frac{2}{3} \cdot \sqrt{6}\right) + 6 \cdot \sqrt{6}\\&=-4 + \left(- \sqrt{2} - \sqrt{3}\right)^{2} + \frac{16}{3} \cdot \sqrt{6}\end{aligned}

+ Submit Question