N-RN: The Real Number System

The Real Number System

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The Real Number System formalizes the distinction between rational and irrational numbers and extends exponent rules to rational exponents. Properties of integer exponents motivate the definition of rational exponents, and these connect radical notation to exponential form. Closure properties of rational and irrational numbers under addition and multiplication are examined and justified.

N-RN.1Explain 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.N-RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents. For example: Write equivalent representations that utilize both positive and negative exponents.N-RN.3Explain 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.
Example Problems
Evaluate:
Simplify:
Is rational or irrational?
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