(o) $$ \frac{\sqrt{48}-\sqrt{32}}{\sqrt{12}-\sqrt{8}} $$

Question

UpStudy AI · Accepted Answer

Let's simplify the expression:

$$
\frac{\sqrt{48} - \sqrt{32}}{\sqrt{12} - \sqrt{8}}
$$

**Step 1: Simplify Each Square Root**

1. $$\sqrt{48}$$:
   $$
   \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
   $$

2. $$\sqrt{32}$$:
   $$
   \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}
   $$

3. $$\sqrt{12}$$:
   $$
   \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
   $$

4. $$\sqrt{8}$$:
   $$
   \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
   $$

**Step 2: Substitute Back into the Expression**

$$
\frac{4\sqrt{3} - 4\sqrt{2}}{2\sqrt{3} - 2\sqrt{2}}
$$

**Step 3: Factor Out Common Terms**

$$
\frac{4(\sqrt{3} - \sqrt{2})}{2(\sqrt{3} - \sqrt{2})}
$$

**Step 4: Simplify the Fraction**

$$
\frac{4}{2} \times \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}} = 2 \times 1 = 2
$$

**Final Answer:**

$$
2
$$
The expression simplifies to 2.

(o) \( \frac{\sqrt{48}-\sqrt{32}}{\sqrt{12}-\sqrt{8}} \)