½[√(3^2 − 3^2 ⁄4) × 3]

asked by guest
on Mar 17, 2025 at 12:25 am



You asked:

Evaluate the expression: 1232−324⋅3\frac{1}{2} \sqrt{{3}^{2} - \frac{{3}^{2}}{4}} \cdot 3

MathBot Answer:

1232−324⋅3=934≈3.89711431702997391043675426838821\frac{1}{2} \sqrt{{3}^{2} - \frac{{3}^{2}}{4}} \cdot 3 = \frac{9 \sqrt{3}}{4} \approx 3.89711431702997391043675426838821

1232−324⋅3=12⋅32−32⋅14⋅3=12⋅9−32⋅14⋅3=12⋅9−94⋅3=12⋅274⋅3=12⋅32⋅3⋅3=34⋅3⋅3=94⋅3\begin{aligned}\frac{1}{2} \sqrt{{3}^{2} - \frac{{3}^{2}}{4}} \cdot 3&=\frac{1}{2} \cdot \sqrt{3^{2} - 3^{2} \cdot \frac{1}{4}} \cdot 3\\&=\frac{1}{2} \cdot \sqrt{9 - 3^{2} \cdot \frac{1}{4}} \cdot 3\\&=\frac{1}{2} \cdot \sqrt{9 - \frac{9}{4}} \cdot 3\\&=\frac{1}{2} \cdot \sqrt{\frac{27}{4}} \cdot 3\\&=\frac{1}{2} \cdot \frac{3}{2} \cdot \sqrt{3} \cdot 3\\&=\frac{3}{4} \cdot \sqrt{3} \cdot 3\\&=\frac{9}{4} \cdot \sqrt{3}\end{aligned}

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