Question

Vocabulary Terms - Define/Illustrate

Square root/Cube root
Repeating decimal
Terminating decimal

Answer 1

Here are definitions and illustrations for the vocabulary terms you mentioned:

### Square Root
- **Definition**: The square root of a number \( x \) is a value \( y \) such that \( y^2 = x \). In simple terms, it is a number that, when multiplied by itself, gives the original number.

- **Illustration**:
- The square root of 16 is 4 because \( 4 \times 4 = 16 \).
- It can be represented mathematically as \( \sqrt{16} = 4 \).

### Cube Root
- **Definition**: The cube root of a number \( x \) is a value \( y \) such that \( y^3 = x \). This means that when \( y \) is multiplied by itself three times, it produces the original number.

- **Illustration**:
- The cube root of 27 is 3 because \( 3 \times 3 \times 3 = 27 \).
- Mathematically, it is expressed as \( \sqrt[3]{27} = 3 \).

### Repeating Decimal
- **Definition**: A repeating decimal is a decimal fraction that eventually repeats a sequence of digits indefinitely. This means that after a certain point, the digits will continue to repeat in the same order forever.

- **Illustration**:
- For example, \( 0.333...\) (where the digit 3 repeats) is a repeating decimal. It can also be shown as \( \frac{1}{3} \).
- Another example is \( 0.1666...\) (where the digit 6 repeats), which can be expressed as \( \frac{1}{6} \).

### Terminating Decimal
- **Definition**: A terminating decimal is a decimal that has a finite number of digits after the decimal point. Thus, it does not continue infinitely and does not have any repeating digits.

- **Illustration**:
- For example, \( 0.75 \) is a terminating decimal, as it has two decimal places and ends there.
- Other examples include \( 1.5 \), \( 2.0 \), and \( 0.125 \).

These terms are fundamental concepts in mathematics, often used in various calculations and number systems.