8.N.1.a Determine subsets of numbers as natural, whole, integer, rational, irrational, or real, based on the definitions of these sets of numbers.
8.N.1.b Represent numbers with positive and negative exponents and in scientific notation.
8.N.1.c Describe the difference between a rational and irrational number.
8.N.1.d Approximate, compare, and order real numbers, both rational and irrational, and locate them on the number line.
8.N.2.a Evaluate the square roots of perfect squares less than or equal to 400 and cube roots of perfect cubes less than or equal to 125.
8.N.2.b Simplify numerical expressions involving integer exponents, square roots, and cube roots (e.g., 4-2 is the same as 1/16).
8.N.2.d Multiply and divide numbers using scientific notation.
8.A.1.c Solve equations of the for where k is a positive rational number, using square root and cube root symbols.
Irrational Number
A number that cannot be written as a fraction and whose decimal goes on forever without repeating. Example: √2 or π
Perfect Square
A number that can be written as a whole number multiplied by itself. Example: 25 is a perfect square because 5 × 5 = 25.
Square Root
A number that, when multiplied by itself, gives the original number. Example: √36 = 6 because 6 × 6 = 36.
Cube Root
A number that, when multiplied by itself three times, gives the original number. Example: ∛27 = 3 because 3 × 3 × 3 = 27.
Perfect Cube
A number that can be written as a whole number multiplied by itself three times. Example: 64 is a perfect cube because 4 × 4 × 4 = 64.
Scientific Notation
A way to write very large or very small numbers using a number between 1 and 10 multiplied by a power of 10. Example: 450,000 = 4.5 × 10⁵
Power of Products Property
When a product is raised to a power, the exponent applies to each factor. Example: (2 × 3)² = 2² × 3²
Product of Powers Property
When multiplying powers with the same base, add the exponents. Example: 3² × 3⁴ = 3⁶
Quotient of Powers Property
When dividing powers with the same base, subtract the exponents. Example: 5⁶ ÷ 5² = 5⁴
Negative Exponent Property
A negative exponent means to take the reciprocal of the base and make the exponent positive. Example: 2⁻³ = 1/2³ = 1/8
Power of Powers Property
When a power is raised to another power, multiply the exponents. Example: (2³)⁴ = 2¹²
Zero Exponent Property
Any nonzero number raised to the zero power equals 1. Example: 7⁰ = 1