math class 678 4-in-1 skill sheets
Operations with Radicals, Algebra 1 4-in-1 Skill Sheet (HSN.RN.A.2)
HSN.RN.A.2 Algebra 1 Unit 8: Exponents and Radicals

Operations with Radicals

I can add, subtract and multiply radicals, and tell when two of them can be combined.

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The problem this sheet solves

Adding radicals keeps the radical and adds only the coefficients, exactly the way like terms work. Multiplication is what joins the radicands. A student who does both at once has applied two correct rules simultaneously, which is far harder to unpick than a simple slip, and simplifying first often changes which radicals are actually alike. This sheet treats radicals as like terms, which connects the new skill to one students already own instead of adding a fresh procedure, and it requires simplifying BEFORE judging whether two radicals can combine. A decimal check is used to settle disputes, since 10.17 against 14.14 needs no argument.

The key rule

Adding keeps the radical and adds only the coefficients, exactly as 2x + 3x = 5x. Multiplication is what joins the radicands. Simplify before you judge.

Add the counts, not the radicands. Simplify first.

Watch out

The mistake: A student writes 2√3 + 3√5 = 5√8.

The fix: 2√3 + 3√5 is already finished: the radicals are unlike. Both halves the student used are real rules in the wrong place — coefficients add when the radicands MATCH, radicands join when you MULTIPLY. In decimals: about 10.17, not 14.14.

What is included

  • Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
  • Practice page — six problems, building from foundational to multi-step
  • Apply page — a word problem, a reasoning prompt, and an error-analysis task
  • Assess — a half-page exit ticket, two to a sheet, with a score box
  • Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
  • Ink-saver edition of all 7 pages
  • 14-slide teacher deck (PowerPoint) with presenter notes on every slide

Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.