Evaluate:
`sqrt(9025)`

Answer

To evaluate \( \sqrt{9025} \), we can follow these steps:

### Step 1: Pair the digits
Start by pairing the digits of the number from right to left. For 9025, we have:
- Pair 1: 25
- Pair 2: 90

### Step 2: Find the largest square less than or equal to the first pair (90)
The largest perfect square less than or equal to 90 is \( 81 \) (which is \( 9^2 \)).

### Step 3: Subtract the square from the first pair
Now, subtract \( 81 \) from \( 90 \):
\[ 90 - 81 = 9 \]

### Step 4: Bring down the next pair (25)
Now, bring down the next pair (25) next to the remainder (9):
\[ 9 \, 25 \]

### Step 5: Double the quotient found so far
The quotient so far is \( 9 \). Double it to get \( 18 \).

### Step 6: Find a digit (let's call it \( x \)) such that \( (18x) \times x \) is less than or equal to \( 925 \)
We need to find \( x \) such that:
\[ (180 + x) \times x \leq 925 \]
Testing \( x = 5 \):
\[ (180 + 5) \times 5 = 185 \times 5 = 925 \]
This is equal to 925, so \( x = 5 \) is valid.

### Step 7: Write the complete quotient
Now, the complete quotient is \( 95 \).

### Step 8: Verify the result
To verify, we can multiply \( 95 \times 95 \):
\[ 95 \times 95 = 9025 \]
Thus, \( \sqrt{9025} = 95 \).

### Final Answer
\[ \sqrt{9025} = 95 \]

---