---
title: "A.NR.5: Radical & Irrational Numbers (Georgia Mathematics standard)"
code: A.NR.5
cite_as: Georgia Standards of Excellence, Mathematics, A.NR.5
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/A.NR.5
md_url: https://georgiahomeroom.org/standards/code/A.NR.5.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/A.NR.5.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# A.NR.5: Radical & Irrational Numbers

Investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- **A.NR.5.1**: Rewrite algebraic and numeric expressions involving radicals.
- **A.NR.5.2**: Using numerical reasoning, show and explain that the sum or product of rational numbers is rational, the sum of a rational number and an irrational number is irrational, and the product of a nonzero rational number and an irrational number is irrational.

## Georgia Milestones coverage

- Algebra I (EOC). Numerical Reasoning. Investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots. (about 10% of the test; 6 points)

## What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

- **Beginning**: Identify the sum of rational and irrational numbers as rational or irrational.
- **Developing**: Rewrite a numeric expression involving radicals. Identify the product of rational and irrational numbers as rational or irrational.
- **Proficient**: Rewrite an algebraic expression involving radicals. Explain why the sum or product of two numbers is rational or irrational.
- **Distinguished**: Solve real-life problems explaining why a sum or product of two numbers is rational or irrational.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.