Math Problem Statement

Solution

The question displayed in the image asks about the type of number 2\sqrt{2}. The options provided are:

  1. Integer
  2. Rational Number
  3. Irrational Number
  4. Whole Number

The correct answer is:

Irrational Number

Here's why: 2\sqrt{2} is a number that cannot be expressed as a fraction of two integers (i.e., pq\frac{p}{q} where pp and qq are integers, and q0q \neq 0). The decimal representation of 2\sqrt{2} is non-repeating and non-terminating. Therefore, it is classified as an irrational number.

Would you like more details or have any questions?

Here are five related questions to expand on this information:

  1. What is the difference between rational and irrational numbers?
  2. Can 3\sqrt{3} be classified as an integer, rational, or irrational number?
  3. How do you prove that 2\sqrt{2} is irrational?
  4. Are all square roots of non-perfect squares irrational numbers?
  5. How can you identify if a given decimal is rational or irrational?

Tip: Any non-perfect square root will result in an irrational number because it cannot be expressed as a simple fraction.