The sum of the perfect squares between 120 and 300 is

Options

A. 1400
B. 1296
C. 1024
D. 1204

Answer

To find the sum of the perfect squares between 120 and 300, we will follow these steps:

### Step 1: Identify the range of perfect squares
We need to find perfect squares that lie between 120 and 300.

### Step 2: Find the smallest perfect square greater than 120
The smallest integer whose square is greater than 120 is 11, since:
- \(11^2 = 121\)

### Step 3: Find the largest perfect square less than 300
The largest integer whose square is less than 300 is 17, since:
- \(17^2 = 289\)

### Step 4: List all perfect squares from \(11^2\) to \(17^2\)
Now we will list the perfect squares from \(11^2\) to \(17^2\):
- \(11^2 = 121\)
- \(12^2 = 144\)
- \(13^2 = 169\)
- \(14^2 = 196\)
- \(15^2 = 225\)
- \(16^2 = 256\)
- \(17^2 = 289\)

### Step 5: Sum these perfect squares
Now we will sum these perfect squares:
\[ 121 + 144 + 169 + 196 + 225 + 256 + 289 \]

Calculating the sum step by step:
1. \(121 + 144 = 265\)
2. \(265 + 169 = 434\)
3. \(434 + 196 = 630\)
4. \(630 + 225 = 855\)
5. \(855 + 256 = 1111\)
6. \(1111 + 289 = 1400\)

### Final Result
The sum of the perfect squares between 120 and 300 is **1400**.

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