The simplified value of 32+488+12is

32+488+12=2×2×2×2×2+2×2×2×2×32×2×2+2×2×3⇒42+4322+23=2(22+23)(22+23)=2

The simplified value of 32+488+12is

32+488+12=2×2×2×2×2+2×2×2×2×32×2×2+2×2×3⇒42+4322+23=2(22+23)(22+23)=2

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The simplified value of $\frac{\sqrt{32} + \sqrt{48}}{\sqrt{8} + \sqrt{12}}$ is

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answer is C.

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Detailed Solution

$\begin{array}{l} \frac{\sqrt{32} + \sqrt{48}}{\sqrt{8} + \sqrt{12}} = \frac{\sqrt{2 \times 2 \times 2 \times 2 \times 2} + \sqrt{2 \times 2 \times 2 \times 2 \times 3}}{\sqrt{2 \times 2 \times 2} + \sqrt{2 \times 2 \times 3}} \\ \Rightarrow \frac{4 \sqrt{2} + 4 \sqrt{3}}{2 \sqrt{2} + 2 \sqrt{3}} = \frac{2 (2 \sqrt{2} + 2 \sqrt{3})}{(2 \sqrt{2} + 2 \sqrt{3})} = 2 \end{array}$