The square root of a positive number less than 100 lies between:

Options

A. 0 and 1000
B. 0 and 10
C. `-10` and 10
D. `-100` and 100

Answer

To solve the problem, we need to find the range of the square root of a positive number that is less than 100. Let's break this down step by step.

### Step 1: Identify the positive number
Let’s denote the positive number as \( x \). According to the problem, we know that:
\[ x < 100 \]

### Step 2: Take the square root
Next, we will take the square root of \( x \):
\[ \sqrt{x} \]

### Step 3: Determine the range of the square root
Since \( x < 100 \), we can find the upper limit for \( \sqrt{x} \) by taking the square root of 100:
\[ \sqrt{100} = 10 \]
This tells us that \( \sqrt{x} \) must be less than 10:
\[ \sqrt{x} < 10 \]

### Step 4: Establish the range of possible values
Since \( x \) is a positive number, \( \sqrt{x} \) must also be positive. Therefore, the range of \( \sqrt{x} \) is:
\[ 0 < \sqrt{x} < 10 \]

### Final Conclusion
Thus, the square root of a positive number less than 100 lies between 0 and 10 (not including 0 and 10):
\[ \text{The range is } (0, 10) \]