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.

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.

Example Problems

Is

\\sqrt{5} + \\sqrt{20}

rational or irrational?

Is

\frac{\sqrt{42}}{\sqrt{6}}

rational or irrational?

Is

\frac{\sqrt{50}}{\sqrt{2}}

rational or irrational?

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