If x is the least number which must be added to 955 to make it a perfect square, then value of 3x + 2 is equal to :

Q: If x is the least number which must be added to 955 to make it a perfect square, then value of 3x + 2 is equal to :

To determine the least number $ x $ that must be added to 955 to make it a perfect square, we first need to find the smallest perfect square greater than 955. 1. **Finding the nearest perfect square:** - Calculate the square root of 955: $\sqrt{955} \approx 30.91$. - The next whole number greater than 30.91 is 31. - Calculate the square of 31: $31^2 = 961$. 2. **Determine $ x $:** - The difference between 961 and 955 gives us the value of $ x $. - $ x = 961 - 955 = 6 $. 3. **Calculate $ 3x + 2 $:** - Substitute $ x = 6 $ into the expression $ 3x + 2 $. - $ 3x + 2 = 3(6) + 2 = 18 + 2 = 20 $. Thus, the value of $ 3x + 2 $ is 20, which corresponds to Option 1. **Explanation for why other options are incorrect:** - **Option 2 (14):** If $ 3x + 2 = 14 $, then $ 3x = 12 $ and $ x = 4 $. Adding 4 to 955 gives 959, which is not a perfect square. - **Option 3 (11):** If $ 3x + 2 = 11 $, then $ 3x = 9 $ and $ x = 3 $. Adding 3 to 955 gives 958, which is not a perfect square. - **Option 4 (5):** If $ 3x + 2 = 5 $, then $ 3x = 3 $ and $ x = 1 $. Adding 1 to 955 gives 956, which is not a perfect square. Therefore, the only correct option is Option 1, where $ 3x + 2 = 20 $.

Question

Accepted Answer

To determine the least number $ x $ that must be added to 955 to make it a perfect square, we first need to find the smallest perfect square greater than 955.

1. **Finding the nearest perfect square:**
   - Calculate the square root of 955: $\sqrt{955} \approx 30.91$.
   - The next whole number greater than 30.91 is 31.
   - Calculate the square of 31: $31^2 = 961$.

2. **Determine $ x $:**
   - The difference between 961 and 955 gives us the value of $ x $.
   - $ x = 961 - 955 = 6 $.

3. **Calculate $ 3x + 2 $:**
   - Substitute $ x = 6 $ into the expression $ 3x + 2 $.
   - $ 3x + 2 = 3(6) + 2 = 18 + 2 = 20 $.

Thus, the value of $ 3x + 2 $ is 20, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (14):** If $ 3x + 2 = 14 $, then $ 3x = 12 $ and $ x = 4 $. Adding 4 to 955 gives 959, which is not a perfect square.
  
- **Option 3 (11):** If $ 3x + 2 = 11 $, then $ 3x = 9 $ and $ x = 3 $. Adding 3 to 955 gives 958, which is not a perfect square.
  
- **Option 4 (5):** If $ 3x + 2 = 5 $, then $ 3x = 3 $ and $ x = 1 $. Adding 1 to 955 gives 956, which is not a perfect square.

Therefore, the only correct option is Option 1, where $ 3x + 2 = 20 $.