Which one of the following sets of surds is in correct sequence of ascending order of their values ?

Options

A. `root(4)(10), root(3)(6), sqrt3`
B. `sqrt3, root(4)(10), root(3)(6)`
C. `sqrt(3),root(3)(6), root(4)(10)`
D. `root(4)(10), sqrt3 , root(3)(6)`

Answer

To determine the correct sequence of surds in ascending order, we need to evaluate the values of the given surds. Let's assume the surds provided are:

1. \( \sqrt{10} \)
2. \( \sqrt[3]{6} \)
3. \( \sqrt{3} \)

We will convert these surds into a comparable form and evaluate their approximate values.

### Step 1: Calculate the approximate values of each surd

1. **Calculate \( \sqrt{10} \)**:
\[ \sqrt{10} \approx 3.162 \]

2. **Calculate \( \sqrt[3]{6} \)**:
\[ \sqrt[3]{6} \approx 1.817 \]

3. **Calculate \( \sqrt{3} \)**:
\[ \sqrt{3} \approx 1.732 \]

### Step 2: Compare the values

Now we have the approximate values:
- \( \sqrt{3} \approx 1.732 \)
- \( \sqrt[3]{6} \approx 1.817 \)
- \( \sqrt{10} \approx 3.162 \)

### Step 3: Arrange the values in ascending order

From the calculated values, we can arrange them in ascending order:
1. \( \sqrt{3} \approx 1.732 \)
2. \( \sqrt[3]{6} \approx 1.817 \)
3. \( \sqrt{10} \approx 3.162 \)

Thus, the correct sequence of the surds in ascending order is:
\[ \sqrt{3}, \sqrt[3]{6}, \sqrt{10} \]

### Final Answer
The correct sequence of surds in ascending order is:
\[ \sqrt{3}, \sqrt[3]{6}, \sqrt{10} \]

---