(-√3 - √2)² -4 -2√6/3 + √6³

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



You asked:

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

MathBot Answer:

\[{\left( -\sqrt{3} - \sqrt{2} \right)}^{2} - 4 - \frac{2 \cdot \sqrt{6}}{3} + {\sqrt{6}}^{3} = -4 + \left(- \sqrt{3} - \sqrt{2}\right)^{2} + \frac{16 \sqrt{6}}{3} \approx 18.9629247804099727201134165478432\]

\[\begin{aligned}{\left( -\sqrt{3} - \sqrt{2} \right)}^{2} - 4 - \frac{2 \cdot \sqrt{6}}{3} + {\sqrt{6}}^{3}& = \left(- \sqrt{3} - \sqrt{2}\right)^{2} - 4 - 2 \cdot \sqrt{6} \cdot \frac{1}{3} + \left(\sqrt{6}\right)^{3}\\& = \left(- \sqrt{2} - \sqrt{3}\right)^{2} - 4 - 2 \cdot \sqrt{6} \cdot \frac{1}{3} + \left(\sqrt{6}\right)^{3}\\& = \left(- \sqrt{2} - \sqrt{3}\right)^{2} - 4 - 2 \cdot \frac{1}{3} \cdot \sqrt{6} + \left(\sqrt{6}\right)^{3}\\& = \left(- \sqrt{2} - \sqrt{3}\right)^{2} - 4 - \frac{2}{3} \cdot \sqrt{6} + \left(\sqrt{6}\right)^{3}\\& = \left(- \sqrt{2} - \sqrt{3}\right)^{2} - 4 - \frac{2}{3} \cdot \sqrt{6} + 6 \cdot \sqrt{6}\\& = \left(-4 + \left(- \sqrt{2} - \sqrt{3}\right)^{2}\right) - \frac{2}{3} \cdot \sqrt{6} + 6 \cdot \sqrt{6}\\& = \left(-4 + \left(- \sqrt{2} - \sqrt{3}\right)^{2} - \frac{2}{3} \cdot \sqrt{6}\right) + 6 \cdot \sqrt{6}\\& = -4 + \left(- \sqrt{2} - \sqrt{3}\right)^{2} + \frac{16}{3} \cdot \sqrt{6}\end{aligned}\]

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