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Operations With Radicals

Operations With Radicals

Recall

A radical with a radicand of x, and an index of n.

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Lesson Goals

  • Add, subtract, and multiply to simplify radical expressions.
  • Simplify radical expressions by rationalizing the denominator.

Try This

Each expression is equivalent to one other expression in the following list.

Identify the pairs of equivalent expressions.

  1. \(\sqrt{2}\left(\sqrt{2}+\sqrt{32}\right)\)
  2. \((5+\sqrt{3})(4-\sqrt{2})\)
  3. \(\sqrt{48}+20-\sqrt{6}-\sqrt{50}\)
  4. \(1-\sqrt{18}+\sqrt{2}-\sqrt{16}\)
  5. \(\sqrt{27}+\sqrt{100}-\sqrt{3}-\sqrt{12}\)
  6. \(\dfrac{1+\sqrt{2}}{1-\sqrt{2}}\)