https://file.aiquickdraw.com/mathbot/file/1727451876298p9m5utum.jpg

To solve this problem, we need to determine which of the square roots are irrational. A number is irrational if it cannot be expressed as a simple fraction, and square roots are irrational if they are not perfect squares.

Let’s analyze each option:

- **A: \(\sqrt{11}\)**  
  \(11\) is not a perfect square, so \(\sqrt{11}\) is **irrational**.

- **B: \(\sqrt{256}\)**  
  \(256 = 16^2\), so \(\sqrt{256} = 16\), which is a rational number.

- **C: \(\sqrt{25}\)**  
  \(25 = 5^2\), so \(\sqrt{25} = 5\), which is a rational number.

- **D: \(\sqrt{181}\)**  
  \(181\) is not a perfect square, so \(\sqrt{181}\) is **irrational**.

- **E: \(\sqrt{3}\)**  
  \(3\) is not a perfect square, so \(\sqrt{3}\) is **irrational**.

### Irrational choices:  
- A: \(\sqrt{11}\)
- D: \(\sqrt{181}\)
- E: \(\sqrt{3}\)

Would you like further explanation or have any questions?

Here are 5 related questions for practice:
1. What is the square root of 169? Is it rational or irrational?
2. Why is the square root of 2 considered an irrational number?
3. Can \(\sqrt{49}\) be classified as a rational number? Why?
4. How would you determine whether \(\sqrt{15}\) is rational or irrational?
5. What are some real-world applications of irrational numbers?

**Tip**: Remember, if the square root of a number doesn't result in an integer, it's irrational!

Learn how to identify irrational numbers by analyzing square roots. This problem focuses on determining whether the square roots of various numbers are irrational by checking if the numbers are perfect squares. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation