How many perfect square numbers are there from 200 to 300 ?

Options

A. A)1
B. B)2
C. C)3
D. D)4

Answer

To find how many perfect square numbers are there from 200 to 300, we can follow these steps:

### Step 1: Identify the range of perfect squares
We need to find the perfect squares that fall between 200 and 300. A perfect square is a number that can be expressed as the square of an integer.

### Step 2: Determine the square roots of the boundaries
- Calculate the square root of 200:
\[ \sqrt{200} \approx 14.14 \]
- Calculate the square root of 300:
\[ \sqrt{300} \approx 17.32 \]

### Step 3: Identify the integers within the range
The integers that fall between the square roots calculated above are:
- The smallest integer greater than 14.14 is 15.
- The largest integer less than 17.32 is 17.

Thus, we will consider the integers 15, 16, and 17.

### Step 4: Calculate the perfect squares of these integers
- Calculate \(15^2\):
\[ 15^2 = 225 \]
- Calculate \(16^2\):
\[ 16^2 = 256 \]
- Calculate \(17^2\):
\[ 17^2 = 289 \]

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

### Step 6: Count the perfect squares
We have found three perfect squares: 225, 256, and 289.

### Conclusion
Thus, the total number of perfect square numbers from 200 to 300 is **3**.