The ascending order of `(2.89)^(0.5) , 2-(0.5)^2 , sqrt3` and `root(3)(0.008)` is

Options

A. `2-(0.5)^2 , sqrt3 , root(3)(0.008), (2.89)^(0.5)`
B. `root(3)(0.008), (2.89)^(0.5), sqrt3, 2-(0.5)^2`
C. `root(3)(0.008), sqrt3, (2.89)^(0.5) , 2- (0.5)^2`
D. `sqrt3, root(3)(0.008) , 2- (0.5)^2, (2.89)^(0.5)`

Answer

To find the ascending order of the given expressions: \( (2.89)^{0.5}, 2 - (0.5)^2, \sqrt{3}, \text{ and } \sqrt[3]{0.008} \), we will evaluate each expression step by step.

### Step 1: Evaluate \( (2.89)^{0.5} \)

The expression \( (2.89)^{0.5} \) represents the square root of 2.89.

\[ (2.89)^{0.5} = \sqrt{2.89} = \sqrt{\frac{289}{100}} = \frac{\sqrt{289}}{\sqrt{100}} = \frac{17}{10} = 1.7 \]

**Hint:** To find the square root of a decimal, you can convert it to a fraction and simplify.

### Step 2: Evaluate \( 2 - (0.5)^2 \)

Next, we calculate \( 2 - (0.5)^2 \).

\[ (0.5)^2 = 0.25 \]
\[ 2 - 0.25 = 1.75 \]

**Hint:** Remember that squaring a number means multiplying it by itself.

### Step 3: Evaluate \( \sqrt{3} \)

Now, we find the value of \( \sqrt{3} \).

\[ \sqrt{3} \approx 1.732 \]

**Hint:** You can use a calculator or approximate values to find the square root of numbers that are not perfect squares.

### Step 4: Evaluate \( \sqrt[3]{0.008} \)

Finally, we calculate \( \sqrt[3]{0.008} \).

\[ 0.008 = \frac{8}{1000} = \frac{2^3}{10^3} \]
\[ \sqrt[3]{0.008} = \sqrt[3]{\frac{2^3}{10^3}} = \frac{\sqrt[3]{2^3}}{\sqrt[3]{10^3}} = \frac{2}{10} = 0.2 \]

**Hint:** The cube root of a fraction can be found by taking the cube root of the numerator and the denominator separately.

### Step 5: Arrange in Ascending Order

Now that we have evaluated all expressions, we have:

1. \( \sqrt[3]{0.008} = 0.2 \)
2. \( (2.89)^{0.5} = 1.7 \)
3. \( 2 - (0.5)^2 = 1.75 \)
4. \( \sqrt{3} \approx 1.732 \)

Now, we can arrange these values in ascending order:

\[ 0.2 < 1.7 < 1.732 < 1.75 \]

Thus, the ascending order of the given expressions is:

\[ \sqrt[3]{0.008}, (2.89)^{0.5}, \sqrt{3}, 2 - (0.5)^2 \]

### Final Answer:

The ascending order is:

\[ \sqrt[3]{0.008}, (2.89)^{0.5}, \sqrt{3}, 2 - (0.5)^2 \]