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!