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Mastering Radical Expressions: Simplify, Add, Subtract, Multiply, Divide

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Learn to simplify, add, subtract, multiply, and divide radical expressions. Identify perfect squares, factorize, and manipulate radicals to find solutions. Practice examples and tips included to enhance understanding.

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Mastering Radical Expressions: Simplify, Add, Subtract, Multiply, Divide

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  1. Standard MCC8EEb Simplify, Add, Subtract, Multiply, and Divide Radical Expressions

  2. Sometimes numbers under the radical sign √, disguise themselves. • First---ALWAYS check to see if they are PERFECT SQUARES—if so, take them out of the radical sign. • Second—check their factors—in other words, what number times what number equals it. • Example----√8 is not perfect BUT you can break it into 4 x 2. AND….4 is PERFECT • SOOOOOOOOOOOOOOOOOOOOO

  3. Break it down! • √8 = √4 x √2 • Then-----√4 becomes a whole number 2 • We write 2 √2. • Ta-dah!!!!! This is your answer!

  4. Another one • √12 = ? X ? where one of the numbers is a perfect square • That’s right---4 x 3 • So, √4 x √3 = √12 • Write √4 as 2 and leave √3 alone

  5. And the answer is….. • 2 √3

  6. Your turn to practice • √18 • √24 • √28 • √40

  7. OK—now just a bit harder…. • Sometimes you miss the largest square. If you do, don’t panic--- • √72----most people say 9 x 8 • √9 x √8 changes to 3 √8 • BUT……..

  8. Watch carefully • √8 breaks into 4 x 2 • 3 √8 continues to break down • Change √8 to 2 √2----take the outside 2 and multiply it by the outside 3 to get 6. • Final answer-----6 √2

  9. Always check your answer….. • 6 √2 means 6 x 6 = 36 • 36 x 2 = 72----the number we started with • You try: • 2√8 • 4 √12 • 3 √18

  10. The answers are…. • 2√8= 4√2 • 4 √12=16√3 • 3 √18= 9√2

  11. Now, there is more to this… • Multiplying radicals is easy—just put together what goes together and always check to see if you can reduce. • √8 x √3 = √24 • √24 = 4 x 6 • Change 4 into 2—leave the 6 in the crazy house • 2 √6

  12. More examples

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