Virginia SOL Math / Algebra I / Expressions & Operations

A.EO.4

Simplifying Radicals

What you'll learn

  • Simplify square-root radical expressions
  • Simplify cube-root radical expressions
  • Multiply and divide simple radical expressions

Words to know

Radical —
an expression using a root symbol, like sqrt(x)
Radicand —
the number or expression under the root
Square root —
a value that, times itself, gives the radicand
Cube root —
a value that, cubed, gives the radicand
Perfect square —
a number like 4, 9, 16, 25 with a whole-number root
Simplest radical form —
no perfect-square factor remains under the root

Why it matters Simplified radicals give exact answers for lengths and distances, such as the diagonal of a square, without rounding.

Worked examples

Model ItI do

Simplify the square root of 72.

Factor out the largest perfect square: 72 = 36 * 2. So sqrt(72) = sqrt(36) * sqrt(2) = 6 * sqrt(2).

Try It TogetherWe do

Simplify the square root of 50.

The largest perfect-square factor of 50 is 25: sqrt(50) = sqrt(25) * sqrt(2) = 5 * sqrt(2).

Now YouYou do

Simplify the cube root of 54.

Look for the largest perfect-cube factor of 54. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Simplify the square root of 25.

  2. 2.Simplify the square root of 8.

  3. 3.Simplify the cube root of 27.

On Level

The core Quick Check from the book.

  1. 1.Simplify the square root of 18.

  2. 2.Simplify the square root of 48.

  3. 3.Simplify the cube root of 8.

  4. 4.Multiply: sqrt(3) * sqrt(12).

  5. 5.Simplify the square root of 100.

Challenge

Stretch your thinking.

  1. 1.Simplify the square root of 75.

  2. 2.Multiply: sqrt(6) * sqrt(8).

  3. 3.Simplify the cube root of 40.