Simplify :-
(i)`(6)/(sqrt(2))`
(ii)`(sqrt(3))/(3)`
(iii)`sqrt((3)/(4))`
(iv)`(6)/(sqrt(2))`
(v)`(sqrt(5))/(10)`
(vi)`sqrt((16)/(2))`

Answer

Let's simplify each of the given expressions step by step.

### (i) Simplify \( \frac{6}{\sqrt{2}} \)

1. Rewrite 6 as \( 3 \times 2 \):
\[ \frac{6}{\sqrt{2}} = \frac{3 \times 2}{\sqrt{2}} \]

2. Rewrite 2 as \( \sqrt{2} \times \sqrt{2} \):
\[ \frac{3 \times \sqrt{2} \times \sqrt{2}}{\sqrt{2}} = \frac{3 \times \sqrt{2} \times \sqrt{2}}{\sqrt{2}} \]

3. Cancel \( \sqrt{2} \):
\[ = 3\sqrt{2} \]

**Final Answer: \( 3\sqrt{2} \)**

---

### (ii) Simplify \( \frac{\sqrt{3}}{3} \)

1. Rewrite 3 as \( \sqrt{3} \times \sqrt{3} \):
\[ \frac{\sqrt{3}}{3} = \frac{\sqrt{3}}{\sqrt{3} \times \sqrt{3}} \]

2. Cancel \( \sqrt{3} \):
\[ = \frac{1}{\sqrt{3}} \]

**Final Answer: \( \frac{1}{\sqrt{3}} \)**

---

### (iii) Simplify \( \sqrt{\frac{3}{4}} \)

1. Rewrite the square root:
\[ \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}} \]

2. Simplify \( \sqrt{4} \):
\[ = \frac{\sqrt{3}}{2} \]

**Final Answer: \( \frac{\sqrt{3}}{2} \)**

---

### (iv) Simplify \( \frac{6}{\sqrt{2}} \)

This is the same as part (i).

1. Rewrite 6 as \( 3 \times 2 \):
\[ \frac{6}{\sqrt{2}} = \frac{3 \times 2}{\sqrt{2}} \]

2. Rewrite 2 as \( \sqrt{2} \times \sqrt{2} \):
\[ = \frac{3 \times \sqrt{2} \times \sqrt{2}}{\sqrt{2}} \]

3. Cancel \( \sqrt{2} \):
\[ = 3\sqrt{2} \]

**Final Answer: \( 3\sqrt{2} \)**

---

### (v) Simplify \( \frac{\sqrt{5}}{10} \)

1. Rewrite 10 as \( 5 \times 2 \):
\[ \frac{\sqrt{5}}{10} = \frac{\sqrt{5}}{5 \times 2} \]

2. Rewrite 5 as \( \sqrt{5} \times \sqrt{5} \):
\[ = \frac{\sqrt{5}}{\sqrt{5} \times \sqrt{5} \times 2} \]

3. Cancel \( \sqrt{5} \):
\[ = \frac{1}{2\sqrt{5}} \]

**Final Answer: \( \frac{1}{2\sqrt{5}} \)**

---

### (vi) Simplify \( \sqrt{\frac{16}{2}} \)

1. Simplify inside the square root:
\[ \sqrt{\frac{16}{2}} = \sqrt{8} \]

2. Rewrite 8 as \( 4 \times 2 \):
\[ = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} \]

3. Simplify \( \sqrt{4} \):
\[ = 2\sqrt{2} \]

**Final Answer: \( 2\sqrt{2} \)**

---

### Summary of Answers:
1. \( 3\sqrt{2} \)
2. \( \frac{1}{\sqrt{3}} \)
3. \( \frac{\sqrt{3}}{2} \)
4. \( 3\sqrt{2} \)
5. \( \frac{1}{2\sqrt{5}} \)
6. \( 2\sqrt{2} \)

---