Evaluate :
`sqrt((14.4)/(22.5))`

Answer

To evaluate the expression \( \sqrt{\frac{14.4}{22.5}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt{\frac{14.4}{22.5}} \]

### Step 2: Eliminate the decimal
To simplify the calculation, we can eliminate the decimals by multiplying both the numerator and the denominator by 10:
\[ \sqrt{\frac{14.4 \times 10}{22.5 \times 10}} = \sqrt{\frac{144}{225}} \]

### Step 3: Factor the numerator and denominator
Next, we can factor the numbers in the square root:
- \( 144 = 12^2 \)
- \( 225 = 15^2 \)

So we rewrite the expression as:
\[ \sqrt{\frac{12^2}{15^2}} = \frac{12}{15} \]

### Step 4: Simplify the fraction
Now, we simplify the fraction \( \frac{12}{15} \):
\[ \frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5} \]

### Step 5: Convert to decimal
To express \( \frac{4}{5} \) in decimal form, we perform the division:
\[ \frac{4}{5} = 0.8 \]

### Final Answer
Thus, the value of \( \sqrt{\frac{14.4}{22.5}} \) is:
\[ \boxed{0.8} \]

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