Find the square root of :
`0.065` correct to three places of decimal.

Answer

To find the square root of 0.065 correct to three decimal places, we can follow these steps:

### Step 1: Convert the decimal to a fraction
We can express 0.065 as a fraction:
\[ 0.065 = \frac{65}{1000} \]

### Step 2: Simplify the fraction
Now, we can simplify the fraction:
\[ \frac{65}{1000} = \frac{13}{200} \]

### Step 3: Find the square root of the fraction
To find the square root of a fraction, we can take the square root of the numerator and the denominator separately:
\[ \sqrt{0.065} = \sqrt{\frac{13}{200}} = \frac{\sqrt{13}}{\sqrt{200}} \]

### Step 4: Calculate the square roots
Now we need to calculate \(\sqrt{13}\) and \(\sqrt{200}\):
- \(\sqrt{13} \approx 3.60555\)
- \(\sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2} \approx 10 \times 1.41421 \approx 14.1421\)

### Step 5: Divide the square roots
Now we can divide:
\[ \sqrt{0.065} \approx \frac{3.60555}{14.1421} \approx 0.254 \]

### Step 6: Round to three decimal places
Finally, we round the result to three decimal places:
\[ \sqrt{0.065} \approx 0.254 \]

### Final Answer:
The square root of 0.065 correct to three decimal places is:
\[ \boxed{0.254} \]

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