The greatest of the numbers `(2.89)^(0.5)`, `2-(0.5)^(2)`, `1+(0.5)/(1-(1)/(2))` , `sqrt(3)` is

Options

A. `(2.89)^(0.5)`
B. `2-(0.5)^(2)`
C. `1+(0.5)/(1-(1)/(2))`
D. `sqrt(3)`

Answer

To find the greatest of the numbers \( (2.89)^{0.5} \), \( 2 - (0.5)^{2} \), \( 1 + \frac{0.5}{1 - \frac{1}{2}} \), and \( \sqrt{3} \), we will evaluate each expression step by step.

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

This expression represents the square root of 2.89.

\[ (2.89)^{0.5} = \sqrt{2.89} = 1.7 \]

**Hint:** Remember that the square root of a number \( x \) can be calculated as \( x^{0.5} \).

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

First, calculate \( (0.5)^{2} \):

\[ (0.5)^{2} = 0.25 \]

Now substitute this back into the expression:

\[ 2 - 0.25 = 1.75 \]

**Hint:** Squaring a number means multiplying it by itself.

### Step 3: Evaluate \( 1 + \frac{0.5}{1 - \frac{1}{2}} \)

First, simplify the denominator \( 1 - \frac{1}{2} \):

\[ 1 - \frac{1}{2} = \frac{1}{2} \]

Now substitute this back into the expression:

\[ 1 + \frac{0.5}{\frac{1}{2}} = 1 + 0.5 \times 2 = 1 + 1 = 2 \]

**Hint:** Dividing by a fraction is the same as multiplying by its reciprocal.

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

The square root of 3 is approximately:

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

**Hint:** You can use a calculator or approximate values to find the square root of a number.

### Step 5: Compare all the evaluated values

Now we have:

- \( (2.89)^{0.5} \approx 1.7 \)
- \( 2 - (0.5)^{2} = 1.75 \)
- \( 1 + \frac{0.5}{1 - \frac{1}{2}} = 2 \)
- \( \sqrt{3} \approx 1.732 \)

### Step 6: Determine the greatest number

Now we compare the values:

- \( 1.7 \)
- \( 1.75 \)
- \( 2 \)
- \( 1.732 \)

The greatest value among these is \( 2 \).

### Final Answer

The greatest of the numbers is \( 2 \).

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