SIMPLIFYING RADICAL EXPRESSIONS



SIMPLIFYING RADICAL EXPRESSIONS Name:_____________________

[pic], read “the square root of 25,” means one of the two positive equal factors of 25.

[pic]; [pic]; [pic]; [pic]

[pic]; [pic]; [pic]; [pic]

[pic] is called a radical, a is called the radicand.

General Rules for Radicals:

[pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic]

Simplifying Square Roots:

Sometimes it is convenient to leave square roots in radical form instead of using a calculator to find approximations (decimal values). Look for perfect squares (i.e., 4, 9, 16, 25, 36, 49, ...) as factors of the number that is inside the radical sign (radicand) and take the square root of any perfect square factor. Multiply the root of the perfect square times the reduced radical. When there is an existing value that multiplies the radical, multiply any root(s) times that value.

Examples:

1. [pic] 2. [pic] 3. [pic]

= [pic] = [pic] = [pic]

= [pic] = [pic] = [pic]

(note that one a comes “out” for each pair of a’s in the radical)

Simplify Completely:

|1. [pic] |2. [pic] |3. [pic] |4. [pic] |5. [pic] |

|6. [pic] |7. [pic] |8. [pic] |9. [pic] |10. [pic] |

|11. [pic] |12. [pic] |13. [pic] | 14. [pic] |15. [pic] |

|16. [pic] |17. [pic] |18. [pic] |19. [pic] |20. [pic] |

|21. [pic] |22. [pic] |23. [pic] |24. [pic] |25. [pic] |

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