Radicals



Radicals

Reminder: What is a perfect square? List the perfect squares from 1 – 225.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, …don’t forget x2, x4, x6, …even exponents

To find the square root of a number is to find one of its two equal factors. Example: [pic] is 5 because 5[pic]5 = 25

Examples:

|[pic] |[pic] |-[pic] |

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|-[pic] |[pic] because 2[pic]2[pic]2 = 8 |[pic]because (-4)(-4)(-4) |

Simplifying Radicals

coefficient[pic]

When you have a radicand that is not a perfect square, you need to break it down into simplest radical form. Break down the radicand into two factors, the largest perfect square that is a factor times a non-perfect square. Then take the square root of the perfect square.

[pic]

[pic][pic][pic]

Take the square root Leave under the radical sign

Examples:

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

| |[pic] | |[pic] | |[pic] |

| |[pic] | |[pic] | |[pic] |

|4. |[pic] |5. |[pic] |6. |[pic] |

| |[pic] | |[pic] | |[pic] |

| |[pic][pic] | |[pic] | |[pic] |

| | | | | |[pic] |

|7.* |[pic]= [pic] |8. |[pic]= [pic] |9. |[pic]= [pic] |

| |[pic] | |[pic] | |[pic] |

| |[pic] | |[pic] | |[pic] |

*Rationalizing the denominator will be taught later Simplifying Radicals

Now try these:

|1. |[pic] |2. |[pic] |

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|3. |[pic] |4. |[pic] |

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|5. |[pic] |6. |[pic] |

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|7. |[pic] |8. |[pic] |

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|9. |[pic] |10. |[pic] |

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|11. |[pic] |12. |[pic] |

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|13. |[pic] |14. |[pic] |

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Simplifying Radicals

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