Which of the following statements is NOT true about irrational numbers. a. Irrational numbers are decimals that have fractional forms. b. Irrational numbers are those roots of radicals that are not perfect. c. Irrational numbers cannot be expressed as quotients of two real numbers. d. Irrational numbers are those decimals that are both non-repeating and non-terminating.

The statement that is **NOT true** about irrational numbers is:

**a. Irrational numbers are decimals that have fractional forms.**

This statement is false because irrational numbers **cannot** be expressed as fractions (i.e., the quotient of two integers). They cannot be written in the form \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \neq 0 \). This is the defining characteristic of **rational** numbers, not irrational numbers.

### Clarifications of the other statements:
- **b. Irrational numbers are those roots of radicals that are not perfect.**  
  This is true. For example, \( \sqrt{2} \) is irrational because it cannot be simplified to a whole number.
  
- **c. Irrational numbers cannot be expressed as quotients of two real numbers.**  
  This is true. Irrational numbers cannot be written as fractions of two integers, and by extension, cannot be expressed as quotients of two real numbers in a simple form.
  
- **d. Irrational numbers are those decimals that are both non-repeating and non-terminating.**  
  This is true. Irrational numbers have decimal expansions that neither repeat nor terminate, like \( \pi \) or \( e \).

Would you like more details on irrational numbers or any other topic? 

Here are 5 related questions:
1. What are examples of common irrational numbers?
2. Can the sum of two irrational numbers be rational?
3. How is the square root of a non-perfect square classified as irrational?
4. How do we prove that \( \pi \) is irrational?
5. Are there any numbers that are neither rational nor irrational?

**Tip:** A quick way to check if a number is irrational is by seeing if its decimal expansion is non-repeating and non-terminating.

Explore the properties of irrational numbers and understand why they cannot be expressed as fractions. This question covers key concepts such as non-repeating, non-terminating decimals, and the difference between rational and irrational numbers. Suitable for students in Grades 9-12.

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