Problem preview

N-RN.3 Warmup M2-062-A03-V03

Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.

Classify a sum of a rational number and an irrational number

Problem

Classify \(1/2+\sqrt{7}\) and give a valid closure argument based on the rational term and irrational term.

Answer choices

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1/2 + √7 is rational because 1/2 is a fraction, and adding a fraction can turn the result into a rational number.

1/2 + √7 is irrational because rational and irrational numbers cannot be added together.

1/2 + √7 is irrational because 1/2 is rational and adding a rational number to an irrational number keeps it irrational.

1/2 + √7 is rational because the square root is being added, not multiplied, so the irrational part does not matter.

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Curriculum context

Course: Math II
Standard: N-RN.3
Category: Number and Quantity
Domain: The Real Number System
Objective: Explain closure properties of rational numbers and irrational results from rational/irrational sums and products.
Problem type: Classify a sum of a rational number and an irrational number