Take factors outside the radical sign
`(i) root3(54(1-sqrt(5))^(3))` `(ii) root5((5-sqrt(5))^(7))`
(iii) `sqrt(8(8)/(63))` `(iv) sqrt(11(11)/(120))`

Answer

Let's solve the problems step by step.

### (i) \( \sqrt[3]{54(1-\sqrt{5})^3} \)

1. **Factor the expression inside the cube root**:
\[ 54 = 27 \times 2 \]
So, we can rewrite:
\[ \sqrt[3]{54(1-\sqrt{5})^3} = \sqrt[3]{27 \times 2 \times (1-\sqrt{5})^3} \]

2. **Separate the cube root**:
\[ = \sqrt[3]{27} \times \sqrt[3]{2} \times \sqrt[3]{(1-\sqrt{5})^3} \]

3. **Calculate the cube roots**:
\[ \sqrt[3]{27} = 3 \quad \text{and} \quad \sqrt[3]{(1-\sqrt{5})^3} = 1 - \sqrt{5} \]
Thus, we have:
\[ = 3 \times \sqrt[3]{2} \times (1 - \sqrt{5}) \]

4. **Final expression**:
\[ = 3(1 - \sqrt{5})\sqrt[3]{2} \]