$$ \frac{ ext { Division }}{ ext { 1) } \frac{\sqrt{32}}{\sqrt{2}}} $$ 2) $$ \frac{\sqrt[3]{51}}{\sqrt[3]{3}} $$ 3) $$ \frac{\sqrt{6}}{\sqrt{3}} $$ 4) $$ \frac{\sqrt{39}}{\sqrt{3}} $$ $$ \begin{array}{ll} ext { 5) } \frac{3 \sqrt{21}}{\sqrt{7}} & ext { 6) } \frac{4 \sqrt{72}}{2 \sqrt{8}}\end{array} $$

Question

$$ \frac{	ext { Division }}{	ext { 1) } \frac{\sqrt{32}}{\sqrt{2}}} $$ 2) $$ \frac{\sqrt[3]{51}}{\sqrt[3]{3}} $$ 3) $$ \frac{\sqrt{6}}{\sqrt{3}} $$ 4) $$ \frac{\sqrt{39}}{\sqrt{3}} $$ $$ \begin{array}{ll}	ext { 5) } \frac{3 \sqrt{21}}{\sqrt{7}} & 	ext { 6) } \frac{4 \sqrt{72}}{2 \sqrt{8}}\end{array} $$

UpStudy AI · Accepted Answer

Let's simplify each of the given division expressions involving square roots and cube roots.

### 1) $$ \frac{\sqrt{32}}{\sqrt{2}} $$

**Simplification:**
$$
\frac{\sqrt{32}}{\sqrt{2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4
$$

**Answer:** $$4$$

---

### 2) $$ \frac{\sqrt[3]{51}}{\sqrt[3]{3}} $$

**Simplification:**
$$
\frac{\sqrt[3]{51}}{\sqrt[3]{3}} = \sqrt[3]{\frac{51}{3}} = \sqrt[3]{17}
$$

**Answer:** $$ \sqrt[3]{17} $$

---

### 3) $$ \frac{\sqrt{6}}{\sqrt{3}} $$

**Simplification:**
$$
\frac{\sqrt{6}}{\sqrt{3}} = \sqrt{\frac{6}{3}} = \sqrt{2}
$$

**Answer:** $$ \sqrt{2} $$

---

### 4) $$ \frac{\sqrt{39}}{\sqrt{3}} $$

**Simplification:**
$$
\frac{\sqrt{39}}{\sqrt{3}} = \sqrt{\frac{39}{3}} = \sqrt{13}
$$

**Answer:** $$ \sqrt{13} $$

---

### 5) $$ \frac{3 \sqrt{21}}{\sqrt{7}} $$

**Simplification:**
$$
\frac{3 \sqrt{21}}{\sqrt{7}} = 3 \times \frac{\sqrt{21}}{\sqrt{7}} = 3 \times \sqrt{\frac{21}{7}} = 3 \times \sqrt{3} = 3\sqrt{3}
$$

**Answer:** $$ 3\sqrt{3} $$

---

### 6) $$ \frac{4 \sqrt{72}}{2 \sqrt{8}} $$

**Simplification:**
$$
\frac{4 \sqrt{72}}{2 \sqrt{8}} = \frac{4}{2} \times \frac{\sqrt{72}}{\sqrt{8}} = 2 \times \sqrt{\frac{72}{8}} = 2 \times \sqrt{9} = 2 \times 3 = 6
$$

**Answer:** $$6$$

---

**Summary of Simplified Expressions:**

1. $$4$$
2. $$ \sqrt[3]{17} $$
3. $$ \sqrt{2} $$
4. $$ \sqrt{13} $$
5. $$ 3\sqrt{3} $$
6. $$6$$
1. 4 2. ∛17 3. √2 4. √13 5. 3√3 6. 6

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