N-RN. The Real Number System

N-RN.A. Extend the properties of exponents to rational exponents.

N-RN.A.1. 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. For example, we define $5^{1/3}$ to be the cube root of $5$ because we want $(5^{1/3})^3 = 5^{(1/3)3}$ to hold, so $(5^{1/3})^3$ must equal $5$.

• Evaluating a Special Exponential Expression
• Evaluating Exponential Expressions
• Extending the Definitions of Exponents, Variation 2

N-RN.A.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

• Checking a calculation of a decimal exponent
• Kepler's Third Law of Motion
• Rational or Irrational?

N-RN.B. Use properties of rational and irrational numbers.

• Calculating the square root of 2
• Coordinates of equilateral triangles
• Rational or Irrational?

N-RN.B.3. 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.

• Operations with Rational and Irrational Numbers
• Sums of rational and irrational numbers