Math Vocabulary Review

Which of the following numbers is classified as an irrational number?

What type of numbers do rational and irrational numbers together form?

Which of the following statements is true about non-perfect square numbers?

Which of the following is NOT an irrational number?

Determine whether the statement 'All non-terminating and non-repeating decimals are irrational numbers' is true or false.

Identify the number that cannot be placed on the number line as an irrational number.

Which of the following statements is false regarding integers?

What is the approximate positive square root of $8$?

Which two rational numbers can be used to bound the number $\sqrt{31}$ within an interval no greater than 0.1?

What is the rational approximation of $2\sqrt{112}$ correct to two decimal places?

What is the correct ordering of the irrational numbers $2\sqrt{112}$, $\sqrt{31}$, $27.3$, and $22$ from greatest to least?

Which of the following numbers is the least when the following real numbers are assessed: $\frac{212}{3}$, $90$, $2\sqrt{49}$, $\sqrt{164}$, and $28.207$?

Which is the correct decimal representation of $\frac{212}{3}$ correct to three decimal places?

Vocabulary

Irrational Numbers: Numbers that cannot be expressed as a ratio of two integers; they often include non-perfect square roots.
Real Numbers: The combination of both rational and irrational numbers represented on the real number line.
Approximation: The process of estimating positive square roots of non-perfect square numbers using rational numbers.

Concepts and Skills

Non-Perfect Squares: Examples provided include 81 (perfect square) and need to determine if 440 and 2460 are non-perfect squares.
Irrational Number Identification: Assessment of if √5 (irrational), 2√36 (rational), and 2.645751311... (irrational) are irrational numbers.

Estimation Techniques

Using Areas of Squares: Estimating irrational numbers like √8, √10, and √15 by visualizing the areas of squares and locating these values on a number line.

True or False Statements

True Statements: Integers are rational numbers and irrational numbers are classified as real numbers.
False Statements: Irrational numbers cannot be expressed in m/n form, and not all non-terminating non-repeating decimals are irrational.

Problem Solving with Irrational Numbers

Intervals: For given irrational numbers (√31 and others), identify intervals with rational numbers that are within 0.1 distance from each number.
Rational Approximations: Create rational approximations of irrational numbers rounded to two decimal places.
Number Line Graphing: Graph the calculated intervals and mark the approximate locations of the irrational numbers.
Ordering Numbers: Arrange irrational numbers from greatest to least using greater than (>) symbols.

Real Number Operations

Decimal Conversion: Convert real numbers (e.g., 212/3, 90, etc.) into decimal form with three decimal places accuracy.
Graphing on Number Line: Each real number must be correctly placed on a real number line for visual representation.
Ordering Real Numbers: List the given numbers from least to greatest using appropriate inequality symbols.

Test your understanding of key mathematical vocabulary in this chapter review. The quiz focuses on concepts such as irrational numbers and their properties. Choose the correct word or phrase to demonstrate your knowledge.