Find the value of question mark(?) in the following questions ?
`sqrt4225+sqrt3136`=?

Options

A. 121
B. 144
C. 125
D. 111

Answer

To solve the expression \( \sqrt{4225} + \sqrt{3136} \), we will find the square roots of each number step by step.

### Step 1: Calculate \( \sqrt{4225} \)

1. **Identify the unit digit**: The unit digit of 4225 is 5. The square of 5 ends with 5, which indicates that the square root will also end with 5.

2. **Estimate the range**: Next, we look for the perfect squares around 4225. The square of 60 is 3600, and the square of 70 is 4900. So, \( \sqrt{4225} \) lies between 60 and 70.

3. **Narrow down the possibilities**: Since 4225 is closer to 4225 than to 3600 or 4900, we can check the squares of numbers in the 60s.
- \( 65^2 = 4225 \)

Thus, \( \sqrt{4225} = 65 \).

### Step 2: Calculate \( \sqrt{3136} \)

1. **Identify the unit digit**: The unit digit of 3136 is 6. The square of 4 ends with 6 (as \( 4^2 = 16 \)) and the square of 6 also ends with 6 (as \( 6^2 = 36 \)). So the square root could end with either 4 or 6.

2. **Estimate the range**: The square of 50 is 2500, and the square of 60 is 3600. Thus, \( \sqrt{3136} \) lies between 50 and 60.

3. **Narrow down the possibilities**:
- \( 56^2 = 3136 \)

Thus, \( \sqrt{3136} = 56 \).

### Step 3: Add the results

Now we can add the two square roots together:

\[ \sqrt{4225} + \sqrt{3136} = 65 + 56 = 121 \]

### Final Answer

The value of the question mark (?) is \( 121 \).

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