Hovedinnhold
Math
Common Core Math
High School: Number and Quantity: The Real Number System
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- Equivalent forms of exponential expressions
- Evaluate radical expressions challenge
- Evaluating fractional exponents
- Evaluating fractional exponents: fractional base
- Evaluating fractional exponents: negative unit-fraction
- Evaluating mixed radicals and exponents
- Evaluating quotient of fractional exponents
- Properties of exponents (rational exponents)
- Properties of exponents challenge (rational exponents)
- Rewrite exponential expressions
- Rewriting exponential expressions
- Simplify square roots
- Simplify square-root expressions
- Simplify square-roots (variables)
- Simplifying exponential expressions
- Simplifying mixed radical and exponential expressions
- Simplifying quotient of powers (rational exponents)
- Simplifying square roots
- Simplifying square roots (variables)
- Simplifying square roots review
- Simplifying square-root expressions
- Solve exponential equations using exponent properties
- Solve exponential equations using exponent properties (advanced)
- Solving exponential equations using exponent properties
- Solving exponential equations using exponent properties (advanced)
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
- Proof: √2 is irrational
- Proof: product of rational & irrational is irrational
- Proof: square roots of prime numbers are irrational
- Proof: sum & product of two rationals is rational
- Proof: sum of rational & irrational is irrational
- Proof: there's an irrational number between any two rational numbers
- Rational vs. irrational expressions
- Sums and products of irrational numbers
- Worked example: rational vs. irrational expressions
- Worked example: rational vs. irrational expressions (unknowns)