$\sqrt{\32}$ $\sqrt{\48}$ / $\sqrt{\8}$ $\sqrt{\12}$

asked by guest
on Dec 27, 2024 at 12:56 am



You asked:

Evaluate the expression: \(\frac{\sqrt{32} \cdot \sqrt{48}}{\sqrt{8} \cdot \sqrt{12}}\)

MathBot Answer:

\[\frac{\sqrt{32} \cdot \sqrt{48}}{\sqrt{8} \cdot \sqrt{12}} = 4\]

\[\begin{aligned}\frac{\sqrt{32} \cdot \sqrt{48}}{\sqrt{8} \cdot \sqrt{12}}& = \sqrt{32} \cdot \sqrt{48} \cdot \frac{1}{\sqrt{8} \cdot \sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot \sqrt{48} \cdot \frac{1}{\sqrt{8} \cdot \sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot 4 \cdot \sqrt{3} \cdot \frac{1}{\sqrt{8} \cdot \sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot 4 \cdot \sqrt{3} \cdot \frac{1}{2 \cdot \sqrt{2} \cdot \sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot 4 \cdot \sqrt{3} \cdot \frac{1}{2 \cdot \sqrt{2} \cdot 2 \cdot \sqrt{3}}\\& = 4 \cdot \sqrt{2} \cdot 4 \cdot \sqrt{3} \cdot \frac{1}{4 \cdot \sqrt{6}}\\& = 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \sqrt{2}\\& = 4\end{aligned}\]

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