Evaluate :
`sqrt((0.225)/(28.9))`

Answer

To evaluate the expression \( \sqrt{\frac{0.225}{28.9}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt{\frac{0.225}{28.9}} \]

### Step 2: Eliminate the decimals
To eliminate the decimals, we can multiply both the numerator and the denominator by 1000 (since 0.225 has 3 decimal places and 28.9 has 1 decimal place). This gives us:
\[ \sqrt{\frac{0.225 \times 1000}{28.9 \times 1000}} = \sqrt{\frac{225}{28900}} \]

### Step 3: Simplify the fraction
Next, we can simplify the fraction:
\[ \sqrt{\frac{225}{28900}} = \sqrt{\frac{225}{289 \times 100}} \]

### Step 4: Factor the numerator and denominator
We know that:
- \( 225 = 15^2 \)
- \( 289 = 17^2 \)
- \( 100 = 10^2 \)

So we can rewrite the expression as:
\[ \sqrt{\frac{15^2}{17^2 \times 10^2}} = \sqrt{\left(\frac{15}{17 \times 10}\right)^2} \]

### Step 5: Remove the square root
By removing the square root, we have:
\[ \frac{15}{17 \times 10} = \frac{15}{170} \]

### Step 6: Simplify the fraction
Now, we can simplify \( \frac{15}{170} \):
\[ \frac{15 \div 5}{170 \div 5} = \frac{3}{34} \]

### Final Answer
Thus, the evaluation of \( \sqrt{\frac{0.225}{28.9}} \) is:
\[ \frac{3}{34} \]

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