Students classify real numbers as natural, whole, integer, rational, or irrational, distinguish rational and irrational values, and represent, compare, and order positive and negative numbers, zero, fractions, decimals, and radicals on a number line. They evaluate square roots of nonnegative perfect squares, simplify square roots by extracting perfect-square factors, and estimate irrational square roots between rational benchmarks to the tenths or hundredths. They add and subtract like square radicals after simplifying them, combining coefficients while recognizing that unlike radicals cannot be combined.
On this page:
- Master skills like “Estimate irrational values”, “Add and subtract like radicals”, and “Compare and order real numbers” with unlimited, free practice problems
- Download (or modify) free worksheets on Real Numbers and Radicals you can use at home or in class with practice problems across all skills in this group including “Represent real numbers on a number line”, “Simplify square roots of perfect squares”, “Distinguish rational and irrational numbers”.
- Start working on adaptive units like “Number Type Classification - Real Numbers - Intro” or “Radicals - Simplifying Intro” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Real Numbers and Radicals: Individual Skills
Master 8 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Add and subtract like radicals
- Classify numbers within the real number system
- Compare and order real numbers
- Distinguish rational and irrational numbers
- Estimate irrational values
- Represent real numbers on a number line
- Simplify radicals containing perfect-square factors
- Simplify square roots of perfect squares
Practice 'Add and subtract like radicals'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
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Download/Modify Free Grade 10 'Real Numbers and Radicals' Worksheet
Print this free 'Real Numbers and Radicals' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Add and subtract like radicals
- Classify numbers within the real number system
- Compare and order real numbers
- Distinguish rational and irrational numbers
- Estimate irrational values
- Represent real numbers on a number line
- Simplify radicals containing perfect-square factors
- Simplify square roots of perfect squares
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Real Numbers and Radicals) through scaffolded problems that grow in difficulty as concepts are understood.