Virginia SOL Math / Algebra II / Expressions & Operations

A2.EO.2

Simplify Radical Expressions

What you'll learn

  • Simplify square and higher-index radicals
  • Factor out perfect powers from a radicand
  • Add, subtract, and multiply like radicals

Words to know

Radical —
an expression using a root symbol, like sqrt(x)
Radicand —
the number or expression under the radical
Index —
the root being taken (2 for square root)
Perfect square —
a number with a whole-number square root, like 36
Like radicals —
radicals with the same index and radicand

Why it matters Simplified radicals are exact values that are easier to compare and combine than long decimals, and they keep answers precise.

Worked examples

Model ItI do

Simplify sqrt(72).

Find the largest perfect-square factor of 72: it is 36, since 72 = 36 * 2. Then sqrt(72) = sqrt(36) * sqrt(2) = 6 sqrt(2).

Try It TogetherWe do

Simplify 3 sqrt(2) + 5 sqrt(2).

These are like radicals, so add the numbers in front: 3 + 5 = 8. The result is 8 sqrt(2).

Now YouYou do

Simplify sqrt(50).

Find the largest perfect-square factor of 50, then take its root. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Simplify sqrt(32).

  2. 2.Simplify 5 sqrt(7) - 2 sqrt(7).

  3. 3.Simplify sqrt(3) * sqrt(12).

On Level

The core Quick Check from the book.

  1. 1.Simplify sqrt(48).

  2. 2.Simplify sqrt(20).

  3. 3.Simplify 2 sqrt(3) + 4 sqrt(3).

  4. 4.Simplify sqrt(2) * sqrt(8).

  5. 5.Simplify sqrt(75).

Challenge

Stretch your thinking.

  1. 1.Simplify sqrt(50) + sqrt(18).

  2. 2.Simplify 2 sqrt(3) * (sqrt(6) + sqrt(3)).

  3. 3.Simplify the cube root of 54 (index 3).