How many perfect squares lie between 120 and 300 ?

Options

A. 5
B. 6
C. 7
D. 8

Answer

To find how many perfect squares lie between 120 and 300, we can follow these steps:

### Step 1: Identify the smallest perfect square greater than 120.
The smallest integer whose square is greater than 120 is 11, since:
- \(11^2 = 121\)

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

### Step 3: List the perfect squares between 121 and 289.
The perfect squares from \(11^2\) to \(17^2\) are:
- \(11^2 = 121\)
- \(12^2 = 144\)
- \(13^2 = 169\)
- \(14^2 = 196\)
- \(15^2 = 225\)
- \(16^2 = 256\)
- \(17^2 = 289\)

### Step 4: Count the perfect squares.
The perfect squares between 120 and 300 are:
- 121
- 144
- 169
- 196
- 225
- 256
- 289

### Step 5: Calculate the total number of perfect squares.
To find the total count of perfect squares, we count the integers from 11 to 17:
- The integers are 11, 12, 13, 14, 15, 16, 17.

So, the count is:
- \(17 - 11 + 1 = 7\)

### Final Answer:
There are **7 perfect squares** between 120 and 300.

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