How many numbers are there between 200 to 300 which are perfect squares?

Options

A. 2
B. 3
C. 4
D. 5

Answer

To find how many perfect squares are there between 200 and 300, we can follow these steps:

### Step 1: Identify the range of perfect squares
We need to find perfect squares of integers that fall between 200 and 300.

### Step 2: Determine the square roots of the boundaries
Calculate the square roots of the lower and upper limits:
- The square root of 200 is approximately \( \sqrt{200} \approx 14.14 \)
- The square root of 300 is approximately \( \sqrt{300} \approx 17.32 \)

### Step 3: Identify the integers within the range
The integers that fall between 14.14 and 17.32 are 15, 16, and 17.

### Step 4: Calculate the perfect squares of these integers
Now, we will calculate the squares of these integers:
- \( 15^2 = 225 \)
- \( 16^2 = 256 \)
- \( 17^2 = 289 \)

### Step 5: List the perfect squares
The perfect squares between 200 and 300 are:
- 225
- 256
- 289

### Step 6: Count the perfect squares
Count the numbers identified:
- There are 3 perfect squares: 225, 256, and 289.

### Final Answer
Thus, the total number of perfect squares between 200 and 300 is **3**.

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