$\sqrt{\32}$/$\sqrt{\2}$/$\sqrt{\48}$/$\sqrt{\12}$

asked by guest
on Dec 27, 2024 at 12:59 am



You asked:

Evaluate the expression: \(\frac{\frac{\frac{\sqrt{32}}{\sqrt{2}}}{\sqrt{48}}}{\sqrt{12}}\)

MathBot Answer:

\[\frac{\frac{\frac{\sqrt{32}}{\sqrt{2}}}{\sqrt{48}}}{\sqrt{12}} = \frac{1}{6} = 0.1\overline{6}\]

\[\begin{aligned}\frac{\frac{\frac{\sqrt{32}}{\sqrt{2}}}{\sqrt{48}}}{\sqrt{12}}& = \sqrt{32} \cdot \frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{48}} \cdot \frac{1}{\sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot \frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{48}} \cdot \frac{1}{\sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \sqrt{2} \cdot \frac{1}{\sqrt{48}} \cdot \frac{1}{\sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \sqrt{2} \cdot \frac{1}{4 \cdot \sqrt{3}} \cdot \frac{1}{\sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \sqrt{2} \cdot \frac{1}{12} \cdot \sqrt{3} \cdot \frac{1}{\sqrt{12}}\\& = 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \sqrt{2} \cdot \frac{1}{12} \cdot \sqrt{3} \cdot \frac{1}{2 \cdot \sqrt{3}}\\& = 4 \cdot \sqrt{2} \cdot \frac{1}{2} \cdot \sqrt{2} \cdot \frac{1}{24}\\& = \frac{4}{24}\\& = \frac{1}{6}\end{aligned}\]

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