3√ 4 × 4√6 / 2√2 × 3√3

asked by guest
on Nov 24, 2024 at 5:36 pm



You asked:

Evaluate the expression: 34⋅4622⋅33\frac{3 \sqrt{4} \cdot 4 \sqrt{6}}{2 \sqrt{2}} \cdot 3 \sqrt{3}

MathBot Answer:

34⋅4622⋅33=108\frac{3 \sqrt{4} \cdot 4 \sqrt{6}}{2 \sqrt{2}} \cdot 3 \sqrt{3} = 108

34⋅4622⋅33=3⋅4⋅4⋅6⋅12⋅2⋅3⋅3=3⋅2⋅4⋅6⋅12⋅2⋅3⋅3=3⋅2⋅4⋅6⋅14⋅2⋅3⋅3=6⋅4⋅6⋅14⋅2⋅3⋅3=24⋅6⋅14⋅2⋅3⋅3=12⋅3⋅3⋅3=36⋅3⋅3=108\begin{aligned}\frac{3 \sqrt{4} \cdot 4 \sqrt{6}}{2 \sqrt{2}} \cdot 3 \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}{4} \cdot \sqrt{2} \cdot 3 \cdot \sqrt{3}\\&=6 \cdot 4 \cdot \sqrt{6} \cdot \frac{1}{4} \cdot \sqrt{2} \cdot 3 \cdot \sqrt{3}\\&=24 \cdot \sqrt{6} \cdot \frac{1}{4} \cdot \sqrt{2} \cdot 3 \cdot \sqrt{3}\\&=12 \cdot \sqrt{3} \cdot 3 \cdot \sqrt{3}\\&=36 \cdot \sqrt{3} \cdot \sqrt{3}\\&=108\end{aligned}

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