Back to Explain operations on rational and irrational numbers — Problem 1 · Task Set 3

Exercises: Explain Why Sums and Products of Rational and Irrational Numbers Follow Specific Rules

Work through each section in order. For explanation problems, write in complete sentences and include the reasoning (proof template, counterexample, or construction). Classification alone is not sufficient — explain why.

Grade 9·21 problems·~32 min·Common Core Math - HS Number and Quantity·standard·hsn-rn-b-3

Work through problems with immediate feedback

Fluency Practice

For each problem, classify the expression and provide the required argument or proof.

Classify $5 + \sqrt{9}$ . (Simplify the radical first.)

Irrational, because it is a sum involving a square root.

Rational, because $\sqrt{9} = 3$ and $5 + 3 = 8$ , which is rational.

Irrational, because adding 5 to a square root always gives an irrational number.

Rational, but only because the rational part (5) is a whole number.