one is asked to say a two digit number.what is the probability of it being a perfect square

To solve this problem, we need to determine the probability that a randomly chosen two-digit number is a perfect square.

### Step-by-Step Solution:

1. **Identify the range of two-digit numbers:**  
   Two-digit numbers range from 10 to 99.

2. **List the perfect squares within this range:**  
   A perfect square is a number that can be expressed as the square of an integer. Let's find the squares of integers that result in two-digit numbers.
   
   - \(4^2 = 16\)  
   - \(5^2 = 25\)  
   - \(6^2 = 36\)  
   - \(7^2 = 49\)  
   - \(8^2 = 64\)  
   - \(9^2 = 81\)
   
   The perfect squares between 10 and 99 are: 16, 25, 36, 49, 64, and 81.

3. **Count the perfect squares:**  
   There are 6 perfect squares in the two-digit range: 16, 25, 36, 49, 64, and 81.

4. **Determine the total number of two-digit numbers:**  
   The total number of two-digit numbers from 10 to 99 is \(99 - 10 + 1 = 90\).

5. **Calculate the probability:**  
   The probability \(P\) of randomly selecting a perfect square is the number of perfect squares divided by the total number of two-digit numbers.

\[
P = \frac{\text{Number of perfect squares}}{\text{Total number of two-digit numbers}} = \frac{6}{90} = \frac{1}{15}
\]

### Conclusion:

The probability of a randomly selected two-digit number being a perfect square is \(\frac{1}{15}\).

Would you like more details or have any questions? Here are some related questions to consider:

1. What is the probability of selecting a perfect cube from the set of two-digit numbers?
2. How many three-digit numbers are perfect squares?
3. What is the probability of randomly choosing a prime number from the set of two-digit numbers?
4. How do you calculate the probability of selecting a number divisible by a specific integer, like 5, from a set?
5. What is the probability of choosing a palindrome from the set of two-digit numbers?

**Tip:** When calculating probabilities involving ranges of numbers, always first identify the total number of outcomes and the specific subset of outcomes that meet your criteria.

Discover how to calculate the probability of selecting a perfect square from two-digit numbers. Learn step-by-step with examples and find out the total number of two-digit numbers and perfect squares. Suitable for Grades 6-8.

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