Simplify : `(2.25)^((1)/(2))`

Options

A. `1.5`
B. 15
C. 1.6
D. `2//3`

Answer

To simplify the expression \( (2.25)^{\frac{1}{2}} \), we can follow these steps:

### Step 1: Convert the decimal to a fraction
We can express \( 2.25 \) as a fraction. Since there are two decimal places, we can write:
\[ 2.25 = \frac{225}{100} \]

### Step 2: Simplify the fraction
Next, we simplify \( \frac{225}{100} \):
\[ \frac{225}{100} = \frac{225 \div 25}{100 \div 25} = \frac{9}{4} \]

### Step 3: Rewrite the expression
Now we can rewrite the original expression using the simplified fraction:
\[ (2.25)^{\frac{1}{2}} = \left(\frac{9}{4}\right)^{\frac{1}{2}} \]

### Step 4: Apply the power of a fraction
Using the property of exponents, we can separate the numerator and denominator:
\[ \left(\frac{9}{4}\right)^{\frac{1}{2}} = \frac{9^{\frac{1}{2}}}{4^{\frac{1}{2}}} \]

### Step 5: Calculate the square roots
Now we calculate the square roots:
\[ 9^{\frac{1}{2}} = 3 \quad \text{and} \quad 4^{\frac{1}{2}} = 2 \]

### Step 6: Combine the results
Now we can combine the results:
\[ \frac{9^{\frac{1}{2}}}{4^{\frac{1}{2}}} = \frac{3}{2} \]

### Step 7: Convert to decimal
Finally, we can convert \( \frac{3}{2} \) to decimal form:
\[ \frac{3}{2} = 1.5 \]

Thus, the simplified value of \( (2.25)^{\frac{1}{2}} \) is \( 1.5 \).

### Final Answer:
\[ 1.5 \]