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Operations with Square Roots Vocabulary

This guide explores the fundamentals of operations with square roots, covering key concepts such as the radical symbol, radical expressions, and the radicand. Learn to simplify radical expressions using the Distributive Property, combining like terms, and applying the Commutative Property effectively. Understand how to multiply radicands and find perfect square factors of the radicand for simplification. With step-by-step examples, this resource is perfect for students looking to enhance their understanding of radicals in algebra.

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Operations with Square Roots Vocabulary

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  1. Operations with Square Roots Vocabulary radical symbol radical expression radicand

  2. A square root symbol, , is called a radical symbol. An expression containing a radical symbol is called a radical expression. The value under a radical symbol is called the radicand. You can use the Distributive Property to combine like terms in radical expressions.

  3. Simplify. The radicands are the same. Combine like terms.

  4. Simplify. Commutative Property Combine like terms.

  5. Simplify. –3 11 + 2 11 ((– 3 + 2) 11 = – 11

  6. Simplify. – 14 + 4 15+ 14 –√14 + √14 + 4 √15= (–1 + 1) √14 + 4√15 = 4√15

  7. Simplify. Multiply the radicands under one radical symbol.

  8. Simplify. Multiply the radicands under one radical symbol.

  9. Simplify. √5 • √20 √5 • 20 = √100 =10

  10. Simplify. √2 • 2√2 2√2 • 2 = 2√4 = 2 • 2 = 4

  11. Simplify. Method A Method B

  12. Simplify. √180 = √180 √36 • 5 = √36 • √5 Possible solution: = 6 5 √

  13. Simplify. Find perfect square factors of the radicand. Simplify. Combine like terms.

  14. Simplify. Find perfect square factors of the radicand. Simplify. Combine like terms.

  15. Simplify. 5√3 – √27 5√3 – √9 • 3 = 5√3 – 3√3 = 2√3

  16. Simplify. 2√24 + 6√54 2√4 · 6 + 6√9 · 6 = 4√6 + 18√6 = 22√6

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