AlgebraStructure & Method · Book 1All Chapters

Radical Expressions

11-8Adding and Subtracting Radicals

Overview

Only like radicals (same radicand) can be combined: a√c + b√c = (a + b)√c.

Key ideas

  • Simplify each radical first.
  • Combine coefficients of like radicals.
  • Unlike radicals stay separate.

Worked examples

Example 1

Problem. Simplify 2√3 + 5√3.

Solution. 7√3

Example 2

Problem. Simplify √8 + √2.

Solution. 2√2 + √2 = 3√2

Practice

Try each one. Click Show answer when ready.

  1. 1.

    4√5 − 2√5

  2. 2.

    √18 + √2

  3. 3.

    √27 − √12

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Simplify 3√8 + 2√18 − √50.

  2. 2.

    Simplify 5√12 − 3√27 + √48.