(3√4 × 4√6) / (2√2 × 3√3)

asked by guest
on Nov 24, 2024 at 5:34 pm



You asked:

Evaluate the expression: \(\frac{3 \cdot \sqrt{4} \cdot 4 \cdot \sqrt{6}}{2 \cdot \sqrt{2} \cdot 3 \cdot \sqrt{3}}\)

MathBot Answer:

\[\frac{3 \cdot \sqrt{4} \cdot 4 \cdot \sqrt{6}}{2 \cdot \sqrt{2} \cdot 3 \cdot \sqrt{3}} = 4\]

\[\begin{aligned}\frac{3 \cdot \sqrt{4} \cdot 4 \cdot \sqrt{6}}{2 \cdot \sqrt{2} \cdot 3 \cdot \sqrt{3}}& = 3 \cdot \sqrt{4} \cdot 4 \cdot \sqrt{6} \cdot \frac{1}{2 \cdot \sqrt{2} \cdot 3 \cdot \sqrt{3}}\\& = 3 \cdot 2 \cdot 4 \cdot \sqrt{6} \cdot \frac{1}{2 \cdot \sqrt{2} \cdot 3 \cdot \sqrt{3}}\\& = 3 \cdot 2 \cdot 4 \cdot \sqrt{6} \cdot \frac{1}{6 \cdot \sqrt{2} \cdot \sqrt{3}}\\& = 3 \cdot 2 \cdot 4 \cdot \sqrt{6} \cdot \frac{1}{6 \cdot \sqrt{6}}\\& = 3 \cdot 2 \cdot \frac{4}{6}\\& = 6 \cdot \frac{4}{6}\\& = \frac{24}{6}\\& = 4\end{aligned}\]

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