Find the square root of :
`0.007225`

Answer

To find the square root of \(0.007225\), we can use the long division method for square roots. Here’s a step-by-step solution:

### Step 1: Pair the digits
Start by pairing the digits of the number from the decimal point. For \(0.007225\), we can pair it as follows:
- \(00 | 72 | 25\)

### Step 2: Find the largest square
Now, we look for the largest square less than or equal to the first pair, which is \(00\).
- The largest square less than or equal to \(0\) is \(0\) (since \(0^2 = 0\)).
- Write \(0\) above the line.

### Step 3: Subtract and bring down the next pair
Subtract \(0\) from \(00\) which gives \(0\). Now, bring down the next pair \(72\):
- Current value: \(00 - 00 = 00\)
- Bring down \(72\) to get \(72\).

### Step 4: Find the next digit
Now, we need to find a digit \(x\) such that \(2 \cdot 0 \cdot x + x^2 \leq 72\).
- Trying \(8\): \(2 \cdot 0 \cdot 8 + 8^2 = 64\) (which is less than \(72\)).
- Write \(8\) above the line.

### Step 5: Subtract again
Now, subtract \(64\) from \(72\):
- \(72 - 64 = 8\).
- Bring down the next pair \(25\) to get \(825\).

### Step 6: Find the next digit
Now, we need to find a digit \(y\) such that \(2 \cdot 8 \cdot y + y^2 \leq 825\).
- \(2 \cdot 8 = 16\), so we need \(16y + y^2 \leq 825\).
- Trying \(5\): \(16 \cdot 5 + 5^2 = 80 + 25 = 105\) (which is less than \(825\)).
- Write \(5\) above the line.

### Step 7: Final subtraction
Now, subtract \(825\) from \(825\):
- \(825 - 825 = 0\).

### Conclusion
Since we have reached \(0\) with no remainder, the square root of \(0.007225\) is \(0.085\).

### Final Answer
\[ \sqrt{0.007225} = 0.085 \]