Module 8 · Radicals · Lesson 34 of 39

Adding and subtracting radicals

Only like radicals combine, so simplify first.

In this lesson · about 10 minutes

  • Recognize like radicals
  • Simplify radicals so they can be combined

Radicals are like terms when they have the same kind of root and the same radicand. Then add or subtract the numbers in front: √3 + 4√3 = 5√3 (the first term's coefficient is an unwritten 1).

√5 − √3 can't be simplified: different radicands. But simplify first, because terms that look different may match: √2 + √8 = √2 + 2√2 = 3√2.

Worked example

Simplify 3√2 + 6√8 − √18

Simplify each radical, then combine like terms.

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    Tip: master each practice set first (get 5 right in a row).

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