Rational and Irrational Numbers. Standards: Use properties of rational and irrational numbers.  MGSE9–12.N.RN.2 Rewrite expressions involving radicals.

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Rational and Irrational Numbers

Standards: Use properties of rational and irrational numbers.  MGSE9–12.N.RN.2 Rewrite expressions involving radicals (i.e., simplify and/or use the operations of addition, subtraction, and multiplication, with radicals within expressions limited to square roots).  MGSE9–12.N.RN.3 Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.

EQ:  Why is the sum or product of rational numbers rational? Why is the sum of a rational number and irrational number irrational? Why is the product of a nonzero rational number and an irrational number irrational?

Real Number System

Definition: Rational Numbers  A number expressible in the form a/b or – a/b for some fraction a/b. The rational numbers include the integers Irrational Numbers A number whose decimal form is nonterminating and nonrepeating. Irrational numbers cannot be written in the form a/b, where a and b are integers (b cannot be zero). So all numbers that are not rational are irrational.

Determine whether Rational or Irrational 24